Courseca

why can't you open a door by pushing its doorknob directly toward or away from its hinges

it is pushing against the axis or rtotation. door pivots abouts its hinges

You are playing basketball and take a shot toward the basket. When the ball is midway to the basket and nothing is touching the ball, what is the direction of the net force on the basketball? [Neglect any effects due to air]

Downward. Explanation: When you are not touching it, the basketball is falling. The only force acting on the ball is its downward weight, so the net force on the ball is downward. The basketball is falling, meaning that it is accelerating downward at the acceleration due to gravity. Gravity affects only the basketball's vertical motion, however, and the ball continues to coast horizontally toward the basket.

You visit a bowling alley and examine the bowling balls that are available for use. They all look identical, but some are heavier (have greater weights) than others. How can you identify the heaviest ball? [Neglect any effects due to air]

Hold the ball motionless in your hand and choose the one that requires the largest upward force to keep it from falling, because to keep a bowling ball from falling, you must push the ball upward with a force that cancels its weight. With your support, the ball is inertial and doesn't accelerate. The heavier the ball, the greater the upward force you must exert on that ball to keep it from falling.

You have shopping cart full of groceries and that cart is on a ramp. You are exerting an uphill force on the cart, so that the net force on the cart is zero. What energy transfer is occurring?

If the cart is moving uphill, you are transferring energy to the cart. If the cart is moving downhill, the cart is transferring energy to you. Explanation: Energy is transferred by doing work and you do work on the cart only when it moves in the direction you are pushing it. Since you are pushing the cart uphill, you do work on it and transfer energy to it only when it moves uphill. Similarly, the cart does work on you only when you move in the direction the cart is pushing you. Since the cart is pushing you downhill, it does work on you and transfers energy to you only when you move downhill.

A downhill skier is descending a snow-covered mountain. The skier steps off of a level region of the mountain and onto a steep slope. The skier begins to accelerate rapidly downhill on the slope. What force is causing the skier to accelerate downhill?

The downhill ramp force that is the sum of the skier's weight and the support force exerted on the skier by the snow-covered slope. Explanation: The skier experiences two individual forces: the skier's weight and a support force exerted on the skier by the snow-covered slope. The skier's weight is directed downward, toward the center of the Earth. The support force acts perpendicular to the slope's surface and therefore is directed up and forward. The skier accelerates in response to the net force, so we must sum those two forces to determine the skier's net force and acceleration. The two forces can't cancel because they don't act in exactly opposite directions. Instead, they only partially cancel and sum to form a ramp force that is directed exactly downhill on the slope. The steeper the slope, the greater the amount of that ramp force and the swifter the skier's acceleration.

Your car has a flat tire and you are using an automobile jack to lift the corner of the car so that you can change the tire. The jack involves a lever and you lift the corner of the car upward by pushing the handle of the lever downward. You notice that as the handle moves downward 10 inches, the corner of the car moves upward only 0.5 inches. Assuming that the jack is not wasting any energy, compare the downward force you exert on the jack handle to the upward force that the jack exerts on the car.

The jack's upward force on the car is 20 times as large as your downward force on the jack handle. Explanation: The work you do on the jack's handle is the same as the work the jack does on the car. Since work is force times distance in the direction of that force, the product of your downward force on the jack's handle times the distance the jack's handle moves downward must be equal to the product of the jack's upward force on the car times the distance the car moves upward. Because the jack's handle moves 20 times as far as the car moves, the jack's upward force on the car must be 20 times as large as the force you exert on the jack's handle.

You have just added a massive stone sculpture to your modern art collection. Unfortunately, the people who delivered the sculpture accidentally set it on its side. What barbarians! To tip the sculpture onto its proper base, you transfer as much momentum as you can to the highest point on the sculpture. You accomplish this transfer (successfully, I might add) by running full speed toward the sculpture and: ??

hitting the highest point on the sculpture with your feet as you jump against it so that you end up reversing you velocity. If you come to a stop due to your impact with the sculpture, you will have transferred all your forward momentum to the sculpture. However, if you jump against the sculpture and reverse your velocity due to your impact, you will have given the sculpture more forward momentum than you had before impact. You will end up heading backward, opposite your original forward velocity, but you will have transferred an exceptionally large amount of forward momentum to the sculpture. By bouncing off the sculpture in this manner, you transfer more forward momentum to the sculpture than you could do by simply coming to rest against it.

suppose the book is completely free of external forces, except for any force you might exert on it yourself. Whuch choice accurately describe the books motion.

if you push the book, its velocity changes. If you stop pushing on the book, it velocity becomes constant. your force on the book causes the book to acclerate. if you do not exert any force on the book, it moves at a constant velocity. It becomes inertial, its experiencing no overall exertnal force, and it coasts.

In what circumstance can you be accelerating forward and still be moving at a constant velocity?

in no circumstance, if you are accelerating, your velocity is changing with time.

You kick a soccer ball (a football) toward the goal. When the fast-moving ball is midway to the goal and nothing is touching it, why is the ball moving toward the goal? [Ignore any effects due to the air or gravity.]

inertia keeps the ball in motion

You've learned to juggle 4 balls at once here on Earth. During a visit to the moon, where the acceleration due to gravity is about 1/6th its Earth value, you decide to try juggling those same 4 balls. You find that, on the moon, each ball has ________________.

less weight and falls more slowly than on earth. it undergoes the same acceleration as on earth when exposed to the same force as on earth. The moon's weaker gravity exerts relatively small downward forces on the ball. The ball's masses--the measures of their inertia--don't depend on gravity and remain unchanged on the moon, each ball accelerates exactly as it did on earth in response to a given force. When the balls are falling, their weaker moon weights act on their unchanged masses and they accelerate downward more slowly than on earth.

in accordance with Newton's third law the forces a ball and a table exert on one another are always equal in amount but opposite in direction. do those two forces ever cancel?

no, although the 2 forces are equal in amount but opposite in direction they act on different objects therefore never cancel. The ball exoerience only one of those forces, namely the force exerted by the table on the ball. That force may well cause the ball to acclerate as it does when the ball bounces on the table

when you toss a ball straight up during the time when the ball is above my hand and heading up, is there a force pushing up on the ball?

no-the ball is still experiencing only one force: its weight, which is directed down. It is moving up not bc something is pushing it up but bc of inertia. In the absence of any force, the ball would coast upward bc of inertia. Because of its weight, the ball can't maintain is constant upward velocity, but it takes time for the ball to stop moving up

You are coasting forward at constant velocity on your inline skates. Suddenly, another skater pushes you so that the net force you are experiencing points toward your left. While your net force points toward the left, your acceleration _______________.

points toward the left (in the direction of your net force

You are traveling on an intergalactic cruise spaceship in deep, gravity-free space. You find that the ship has a bowling alley! Once again, there are many identical-looking balls available for use. Without gravity, however, they all have the same weight: zero. How can you identify the ball that will be heaviest when your cruise ship lands on a planet and gravity is present? [Neglect any effects due to air]

shake each ball rapidly back and forth, and choose the ball that accelerate the least in response to the same force as on earth, Without gravity the bowling ball has no weights, but still have masses. Each ball's weight on earth or another planet will be proportional to its mass. The most massive ball will be the heaviest ball when gravity is restored. To find the most massive ball, you can exert forces on the balls and observe their accelerations. The most massive ball will be the one that accelerates least in response to gravity.

** suppose you and your child half your height lean out over the edge of a swimming pool at the same angle. if you both let go and tip into the water who hits first

shorter child, you weigh twice as muchas the child and you weight, which effectlevly acts at your center of gravity i located twice as far from your feet as for the child. Therefore you experience 4x as much gravitational torque about your feet as the child experience

While searching for your keys, you place your cup of coffee on the roof of your parked car. Unfortunately, you forget about the coffee and climb into the car without it. As you start driving the car forward, you hear the coffee hit the ground behind the car. Why didn't the coffee stay on the roof of the car?

the coffee's inertia kept it essentially motionless as the car accelerated forward and left the coffee behind

The chef at a pizza restaurant tosses a spinning disk of pizza dough into the air. As the disk stretches outward in midair and its diameter increases, what happens to the disk's angular momentum and angular velocity about the disk's center of mass? [Note that the disk's weight, which acts at the disk's center of gravity, produces zero torque on the disk about the disk's center of mass. Ignore any effects due to the air.]

the disk's angular momentum is constant, but the disk's angular velocity decrease. The disk is isolated from external torques so its angular momentum is constant. AS the disk's diameter increases, its mass shifts father from its center of mass (the center of rotation so the disk's rotational mass increases. For the disk's angular momentum to remain constant as its rotational mass increases, the disk's angular velocity must decrease. Because the disk is not rigid, Newton's 1st law of rotation doe not apply to it.

A diver stands upright at the edge of the 10 meter platform at the Olympics. The diver jumps off the platform, folds into a ball shape, completes 3.5 somersaults, unfold out of the ball shape, and plunges head-first into the water. Compare the diver's angular momentum about the diver's center of mass at three different moments while that diver is not touching anything: (a) before folding into a ball shape, (b) while ball-shaped, and (c) after unfolding out of the ball shape [Note that the diver's weight, which acts at the diver's center of gravity, produces zero torque on the diver about the diver's center of mass. Ignore any effects due to the air.]

the diver's angular momentum is the same at all 3 moments.When the diver is not touching anything, the diver is experiencing zero torque about the diver's center of mass and cannot be exchanging angular momentum with anything else. The diver's angular momentum is therefore constant throughout the dive.

when a box slide to a stop on a motionless floor, which object does work on the other

the floor does negative work on the box--the floor doesnt move so the box cannot do any work on it, positive or negative. the box does move and the floor pushes the box in the direction opposite the box's velocity. floor therefore does negatve work on box.

which force is your weight?

the force that causes you to accelerate downward when you are high above the surface of a trampoline, because your weight is the force of earth's gravity exerts on you. When no other forces are acting on you, your weight causes you to accelerate down

A set of dishes sits motionless on a slippery silk tablecloth. If you pull the tablecloth sideways quickly, it will slide out from under the dishes and leave the dishes almost unaffected. Why won't that same result occur if you pull the tablecloth sideways slowly?

the moving tablecloth exerts small forces on the dishes, and given enough time, those forces will overwhelm the inertia and causes the dishes to move with the tablecloth

how does a bottle opener use mechanical advantage to pry the top off a soda bottle?

the use of the lever magnifies the force applied to the end of the bottle opener.

suppose youre carrying a ball in your hand as you walk forward at a constant velocity. which physical quantity are you most aware of

A: the ball's weight. to keep the ball from falling you must support its weight and you are aware of that weight. since the ball is moving at constant velocity however you are unaware of its mass

The front wheel of your bicycle spins freely on its axle and rotates at almost constant angular velocity if nothing outside the bicycle exerts a torque on it. Suppose the front wheel is motionless as you stand next to your bicycle. You get on the bicycle and pedal forward. As the bicycle begins to move forward, why does its front wheel begin to rotate?

the ground exerts a backward static frictional force on the bottom of the front wheel to prevent that whee from sliding across the ground. That frictional force, exerted at a lever arm from the wheel's center of rotation, produces the torque that causes the wheel to begin rotating. It was motionless before you started forward and in the absence of friction with the ground, that front wheel will remain motionless. But the ground and front wheel do exert frictional forces on one another and as the bike begins to move forward the bottom of that wheel threatens to slide forward across the ground. To prevent the start of that sliding, the ground exerts a backward static frictional force on the bottom of the wheel. That friction force successfully prevents sliding, but it also produces the torque that causes the wheel to start spinning

a common pair of plier has a place for cutting wires, bolts or nails. why is it so important that this cutter be located very near the plier's pivot

the largest force will be exerted closer to the point of pivot this will allow for the least amount of force to be applied on the lever side of the wires

Pedaling your bicycle provides power to its rear wheel and propels your bicycle forward. What force(s) is principally responsible for the bicycle's forward acceleration as you pedal your bicycle forward from rest on a level (horizontal) road?

the pavement exerts a forward firctional force on the bottom of the rear wheel. as you pedal your bike you are providing power to its rear and causing rear wheel to spin. As the rear wheel begins to spin, the bottom of that wheel threatens to slide backward across the road pavement. To prevent the start of that sliding, the pavement exerts a forward static frictional force on the bottom of the wheel. That forward frictional force successfully prevents sliding, but is also pushes the entire bike forward and causes it to accelerate forward.

Two skaters are coasting forward across the ice. The skater in red has a greater mass than the skater in blue. You begin pushing the two skaters forward with equal forces. How do they move while you are pushing them? [The correct answer must always be true, no matter how fast the skaters were moving before you began pushing them.]

the skater in red experiences less acceleration than the skater in blue

You are riding on a large carousel at an amusement park and you are enjoying the moving scenery as the carousel spins about its center of rotation. The ride comes to an end and the carousel gradually slows to a stop. Why does it take so long for the carousel to stop rotating?

the spinning carousel carries a large amount of angular momentum and the angular impulse needed to remove that angular momentum with a reasonable torque requires a long time. The spinning carousel carries angular momentum (conserved) when the ride ends, the carousel must transfer its large angular momentum to something else in order to slow it to a stop. It must do an angular impulse on something else. That angular impulse is the product of the torque it exerts and the duration of that torque. To avoid having to exert an enormous possible dangerous torque on whatever stop the carousel. the carousel stops slow,

To win a big prize at the fair or festival, all you have to do is toss a basketball into a bucket located about 10 feet (3 meters) in front of you and have the basketball remain in the bucket. The rigid bucket cannot move and it opens toward you. However, the bucket is tilted upward just enough that the basketball will remain in it if someone places the basketball in the bucket by hand. You try a dozen times to get the basketball to stay in the bucket, but it keeps bouncing back out of the bucket. Why is it so difficult for the basketball to come to rest in the bucket?

to stop moving, the basketball must transfer both energy and momentum to the bucket and while it transfer momentum easily to the bucket, it transfers almost zero energy to the bucket. The fast moving basketball carries energy and momentum as it approaches the bucket and it must get rid of both of those conserved quantities in order to stop moving. During its impact with the bucket the basketball transfer momentum easily to the bucket by way of an impulse, it exerts a force on the bucket for time. Because the bucket is rigid and immovable, the basketball is unable to do any significant work on the bucket, it exerts a force on the bucket but the bucket barely moves any distance in the direction of that force. The basketball therefore cannot transfer any significant energy to the bucket, instead of stopping in the bucket, the basketball bounces out of the bucket. It retains nearly all its original energy, but it reverse its direction and therefore its momentum.

A car traveling at 60 mph (100 km/h) veers off the road and hits a tree. The car immediately comes to a complete stop. Fortunately, the airbag inflates and the driver comes to a stop in the airbag instead of coming to a stop on the steering wheel. Hitting the airbag rather than the steering wheel saves the driver's life because the driver

transfers all her momentum to whatever stop her, but that transfer is slower and involves a smaller force when she hits the airbag. While the car and driver are moving forward, the driver carries several quantities with her. One is momentum, and the driver's momentum is directed forward. Force is not a conserved quantity and exerted between objects rather than carried by individual objects. While the momentum-transferring impulse she did to the airbag was the same as the impulse she would have done to the steering wheel, the airbag impulse took more time and therefore involved a smaller, safer impact force.

when a large steel bolt has rusted in place you may have trouble unscrewing it. why does using a larger wrench make it easier to unscren the bolt

with a longer lever arm, the force you exert on the wrench produces more torque on the bolt. the torque you exert on the bolt about the center of rotation is the product of your force times the lever arm extending from the center of rotation to the point where you force acts, with its longer handles the larger wrench is prociding you with a longer lever arm and allowing you froce to produce more torque about the center of mass

**can a table ever exert an upward force on ana egg that is greater in amoint than the egg's weight

yes, the support force that the table exerts on the egg is independent of the egg's weight and can have almost any value. Only when the egg is supported motionless by the table is the table's support force equal in amount to the egg's weight. if you drop the egg on the table, there are times when the tables support force on the egg is much greater in amount than the egg's weight and it may well break the egg's shell.

why can't you open by pushing on its hinged sides

you may be producing a force by this force generates no torque

If a toaster is labeled as using 1000 wats, how much energy does it consume in 1 hour?

3,600,000 J. the watt is a unit of power, equal to the joule per second. if it consumes 1000 watts, meaning that it consumes 1000 joules per second. In 1 second your toaster consumes 1000 J of energy, in 2 seconds 2000 J and so on. In 1 hour (3600 seconds) it consumes 3,600,00 J

You are playing volleyball and your teammate has just hit the ball forward -- toward your opponents. To increase the ball's forward speed, you push it with a forward force of 200 newton (45 pounds-force). What force, if any, does the ball exert on you?

A backward force of 200 newtons. Explanation: Regardless of the volleyball's motion, the force it exerts on you is exactly equal in amount to the force you exert on it, but in the opposite direction. That perfect pairing of forces is recognized in Newton's third law of motion: the force you exert on the volleyball and the force the volleyball exerts on you are equal in amount but opposite in direction.

Most cars have mechanical brakes on all 4 of their wheels. Each of these brakes has two surfaces, one that rotates with the wheel and one surface that doesn't rotate. When you begin to brake, these 2 surface begin to slide across one another. The harder you press the brake the more tightly those surface are pressed against one another. Why do the brakes permit the 2 surfaces to slide across one another, rather than locking those 2 surface together so that they don't slide across one another?

-The purpose of brakes is to waste the moving car's kinetic energy, using sliding friciton, and thereby slowing the car safely. Locking the brakes would result in static friction in the brakes themselves from wasting more than a tiny fraction of the car's kinetic energy. A moving car carries kinetic energy. To slow that car you must get rid of that kinetic energy. Most car simply grind their kinetic energy up into thermal energy. They use sliding friction in their brakes to waste their kinetic energies, since static friction does not waste energy, locking the brakes would be counterproductive and cause the kinetic energy to go somewhere else instead. Most likely that energy would be ground up into thermal energy as the suddenly motionless wheels skidded across the pavement. A skidding car doesn't stop instantly, it decelerates gradually in response to the weaker forces of sliding friction that the pavement exerts on the skidding tired. Permitting the brake surface to slide allows them to waste the car's kinetic energy, avoid wear in the tires and pavement, maintain steering and probably stops the car more quickly. The car's rolling wheels obtain the strong forces of static friction from the pavement and decelerate the vehicle more rapidly.

suppose you drop a stone off a seeaside cliff and it takes 2 sec for the stone to fall into the water below. After only 1 sec of falling approx where was the stone located

-much closer to your hand than the water: the stone's average spped during the 1st second of falling was much smaller than its average speed during the 2nd second of falling. The stone only traveled one quarter of the way down from your hand during that 1 second and completed the remaining three quarters of its travel during the second second.

you hold one end of a rubber band motionless with your left hand and stretch the rubber band with your right hand. which of your hands are/is transferring energy to the rubber band.

-only the right hand is transferring energy to the rubber band. you transfer energy by doing work. to do work on a portion of the rubber band, you must exert a force on that portion and that portion must move a distance in the direction of your force. although your left hand does exert a force on the portion of the rubber band it touches, that portion of rubber band does not move, therefore your left hand does not work on the band.

what is direction of his velocity and acceleration as he climbs the stairs

-velocity pointed up the stairs, acceleration pointed down the stairs. He was slowing down though, so he was accelerating in the direction opposite his velocity, which was down

While vacationing on a tropical island, you find the courage to step off a high cliff and fall for 4 seconds before entering the water below. Exactly 2 seconds into your fall, you glance at the cliff face and see a secret treasure embedded in the rock. When you recover from your plunge, you return to the cliff top and find that treasure ______________________.

1.4 the distance down the cliff top to the water. Explanation: As you fall, you accelerate downward at the acceleration due to gravity and your velocity increases steadily in the downward direction. You cover more and more downward distance with each passing second. During the first half of your fall (the first 2 seconds), your average downward velocity is small and you move downward only 1/4 of the distance from the cliff top to the water. During the second half of your fall, however, your average speed is much greater and you move downward the remaining 3/4 of the distance from the cliff top to the water. Since you saw the treasure only 2 seconds into your fall, it must be located much closer to the cliff top than to the water.

***If you throw a ball directly upward at 10 meters-per-second (22 mph), it will rise upward about 5 meters before coming momentarily to a stop. If you throw that ball directly upward at 20 meters-per-second (44 mph), how far will it rise upward before coming momentarily to a stop?

20 meters, by throwing the ball up you are causing the ball to transform its kinetic energy into gravitational energy. Since the kinetic energy in a ball's translation motion is proportional to square of its speed, the 20 m/s ball has 4 times a much kinetic energy as the 10 m/s ball. That ball's gravitational potential energy is proportional to it altitude, so with 4 times a much kinetic energy, the 20 m/s ball can rise 4 times a far as the 10 m/s ball or 20 m upward.

At a track and field competition, the runners in a 100 meter spring race start with their feet pressed against the nearly vertical metal surfaces of the starting blocks and their shows have shae spikes that project into the track as they run. Why are the starting block and spikes important to the runners in the 100 meter spring.

A: to win, a runner needs an enormous forward acceleration. Starting blocks help by exerting large forward-directed support forces on the runners, and spikes increase the forward static fricitonal foces that eh track can exert on them. The nearly vertical surfaces of the starting blocks can exert support forces on the runners' feet at the start of the race. As the runners push back on their start blck , their feet and their starting block begin to exert support forces on one another in order to prevent them from occupying the same space at the same time. Aided by the large forward forces, the runners acclerate forward rapidly. During the middle of the race, the only forward forces available to the runners are frictional forces from the horizontal track. With the aid of spikes, those frictional forces can be quite large and allow runners to continues their rapid forward accelration

You throw a handful of different coins up and forward and watch them arc through space. They leave your hand at the same moment and with the same starting velocity. Neglecting any effects due to air, where and when do those coins hit the level ground in front of your feet? [Note: air can significantly affect fast-moving coins. If you want to test your answer experimentally, be careful to minimize those air effects. Also, be safe!]

All the coins hit the ground at the same time and at the same distance from your feet. Explanation: After the coins leave your hand, they are falling vertically while coasting horizontally. Since each coin's weight is proportional to its mass, they all accelerate downward equally, at the acceleration due to gravity. Since they had the same vertical component of velocity when they left your hand, they rise and fall together, and hit the ground simultaneously. While they are falling, the coins are also coasting horizontally. When you threw them, you gave them all the same horizontal component of velocity and they retain that horizontal component of velocity until they hit the ground. Since they're all coasting horizontally at the same speed from the same starting point, and they hit the ground at the same moment, they all land together and at the same distance from your feet.

You are shopping in a store and want to go upward from the second floor to the third floor. You can make that trip using an escalator, an elevator, or a staircase. Which method of going from the second floor to the third floor will increase your gravitational potential energy the most?

All three methods will increase your gravitational potential energy by the same amount. Explanation: Your increase in gravitational potential energy depends only on your increase in altitude. In this case, that altitude increase is the upward distance from the second floor to the third floor. How you accomplish this increase in altitude doesn't matter. The work required to lift you from the second floor to the third floor is the same for all three methods, because that work becomes your increased gravitational potential energy. The elevator, the escalator, and your legs all do the same work on you in lifting you from the second floor to the third floor. In the latter case, your legs convert your chemical potential energy into your gravitational potential energy, so your total energy doesn't change. However, the question asked only about the increase in your gravitational potential energy.

When you stand and remain motionless on a bathroom scale, what force is the scale exerting on your feet?

An upward support force equal in amount to your weight. Explanation: To remain motionless, you must be experiencing zero net force. Since your downward weight hasn't vanished, the scale must be exerting an upward force on you equal in amount to your weight. Those two forces, equal in amount but oppositely directed, sum to zero and you are thus experiencing zero net force. Incidentally, the scale measures the force it exerts on you in this situation and reports that force as its determination of your weight.

A good 10 year old baseball pitcher can thrown a 50 mph fastball, but it takes a world-calss pitcher to thrown a 100 mph fastball. How do the energy in those two fastballs compare.

The 100 mph fastball carries 4x as much Kinetic energy as the 50 mph. The kinetic energy an object carries in its translation motion is proportional to the square of its spped. a 100 mph baseball therefore carries 4x as much KE as a 50 mph ball. The pitcher must not only give the ball 4x as much energy, but must transfer that energy to the ball in about half the time. Overall, the pitcher of the 100 mph fastball provides about 8x as much power during the pitch as the pitcher of the 50 mph fastball

When an archer sends an arrow toward a target, the archer must aim the arrow above the target's bullseye (its center) in order for the arrow to hit that bullseye. If the archer uses a stronger bow and therefore a faster-moving arrow, how will that change how the archer aims the arrow in order to hit the same target's bullseye? [Neglect any effects due to air]

The archer must still aim above the target's bullseye, but less far above the bullseye than with the slower-moving arrow. Explanation: After the arrow leaves the bow, the only force acting on the arrow is its weight and it accelerates downward at the acceleration due to gravity. It falls vertically as it coast horizontally. During its brief trip from bow to target, the arrow undergoes a change velocity: the vertical component of that velocity increases in the downward direction. Instead of traveling in a straight-line path, therefore, the arrow arcs slightly downward and hits the target below the point at which the archer was aiming the arrow. Increasing the arrow's speed, however, shortens the duration of the arrow's trip and therefore the time the arrow has to fall. The faster-moving arrow undergoes a smaller change in its velocity and follows a straighter path. Although it still arcs slightly downward before hitting the target, it arcs less than the slower-moving arrow. The archer must still aim above the target's bullseye, but not as far above the bullseye as for the slower-moving arrow.

As you collect plastic bottles for recycling, one of the bottles rolls horizontally off the kitchen counter and bounces on the floor about 1 foot (0.3 meters) outward from the base of the counter. Why didn't the bottle drop straight down and hit the floor exactly at the base of the counter?

The bottle coasted horizontally outward as it fell vertically. Explanation: Once the bottle leaves the counter, it begins to fall and its vertical motion is that of a falling object. But the bottle also had a horizontal component to its velocity when it left the counter and it continues to coast horizontally until it hits the floor. The bottle evidently had enough horizontal speed to carry it 1 foot (0.3 meters) outward from the counter before the bottle reached the floor.

You are in an ordinary room (both its floor and ceiling are horizontal). You throw a ball directly upward and it bounces off the ceiling. While the ball is touching the ceiling, in which direction is the ceiling's support force on the ball?

The ceiling's support force on the ball is directed downward. Explanation: The ceiling and ball exert support forces on one another to prevent them from occupying the same space at the same time. Since their overlap gets worse as the ball moves upward, the ceiling's support force acts downward on the ball as they touch.

You are arm-wrestling another friend and find that you are almost perfectly matched. Your pair of arms is vertical and motionless, even though you are both trying hard to win. To begin winning, you want that pair of arms to rotate counterclockwise from your perspective. What must you do to make that happen?

The counterclockwise torque you exert on the pair of arms must be greater in amount than the clockwise torque your friend is exerting on that pair. Explanation: In effect, the two of you are twisting an object—your pair of arms—in opposite directions. While that pair is vertical and motionless, the net torque it experiences is zero and it is rotationally inertial—the pair of arms is motionless and remains motionless. If you increase the torque you exert on the pair, however, the net torque on the pair is no longer zero and it undergoes angular acceleration. Its angular velocity increases in the direction that you want in order to win.

You are making pizza and are spinning a ball of pizza dough in midair to make a larger and larger disk. As the diameter of the disk increases, you find it more difficult to change the disk's angular velocity. Why?

The disk's rotational mass increases with its diameter, although its mass remains unchanged. Explanation: The dough's mass doesn't depend on its shape, but its rotational mass does. The larger the disk's diameter, the farther the dough's mass is from its center of rotation—which, for a disk in midair, is its center of mass. Moving the disk's mass outward from its center of rotational increases that disk's rotational mass and makes it less responsive to torques. As the disk's rotational mass increases, the disk undergoes a smaller angular acceleration in response to the same net torque.

A tall luxury hotel has a rotating restaurant at its top. The disk-shaped floor of the restaurant rotates slowly about the center of the restaurant and completes one full rotation every 30 minutes. When the restaurant opens each day, the manager turns on the motors that make the restaurant spin, but it takes several minutes for the restaurant to begin spinning at its full angular velocity. Why doesn't the restaurant reach full speed immediately?

The restaurant's angular acceleration is proportional to the net torque exerted on it. The motors produce a net torque on the restaurant and it immediately undergoes angular acceleration. But it takes time for the angular-accelerating restaurant to reach its full angular velocity. Explanation: A net torque causes angular acceleration, not angular velocity. In this case, the net torque on the restaurant causes the restaurant's angular acceleration. Opposing that angular acceleration is the restaurant's enormous rotational mass—the measure of its rotational inertia. Although the motors produce a large net torque on the restaurant, the restaurant's rotational mass is so huge that the restaurant's angular acceleration is still small. Since angular acceleration is the rate at which angular velocity is changing with time, the restaurant's angular velocity changes gradually with time. It takes a few minutes, but the restaurant's angular velocity eventually reaches its full operating value.

An African swallow is flying east at 60 mph (about 100 km/h) and a European swallow is flying west at 60 mph (about 100 km/h). These two swallows have _______________.

The same speed but different velocities

You are traveling through deep space in a large spaceship and everything in the ship is weightless. The ship is experiencing zero net force and it coasts forward. However, in preparation for docking at a space station, the ship is rotating slowly. You notice that one location in the coasting ship moves at constant velocity, even as the rest of the ship rotates about that location. What is this special location in the ship?

The ship's center of mass. Explanation: This question focuses on the ship's inertial behavior and therefore on its center of mass. The ship's center of mass is the effective location of the ship's total mass. The ship's motion can be separated into two parts: the translational motion of its center of mass and its rotation about its center of mass. Because the net force on the ship is zero, the ship's center of mass travels at constant velocity. At the same time, the ship can rotate about that center of mass. Actually, if the ship isn't wobbling, then it rotates about an axis that passes through the center of mass, but there are other locations along that rotation axis that also travel at constant velocity. However, if the ship's captain changes the ship's rotational axis (something that can be accomplished using rocket engines), the new rotational axis will still pass through the ship's center of mass. That behavior makes the center of mass unique—it's the only location in the ship that always travels at constant velocity when the net force on the ship is zero.

The harder you press on an car's brakes, the greater the support forces that the 2 surfaces in each brake exert on one another. Why does this increase in support forces in the brakes result in more rapid deceleration (acceleration opposite its velocity) of the car?

The sliding frictional forces the 2 brake surfaces exert on one another are approx. proportional to their support forces on one another. As the support forces increase, the sliding frictional forces also increase they waste the car's kinetic energy faster, so that is slow more quick. The stronger support forces in the brakes result in stronger frictional forces in the brakes, so that the brakes slow the car more quickly. A car decelerates when the net force it experiences is directed opposite its velocity. during braking the decelerating part of the net force comes from the static frictional forces exerted by the pavement on the car's tires the car brakes' act to slow the rotation of its wheel so the pavement respond by trying to keep those wheels rotating. The brakes use sliding frictional forces to slow the wheel and those forces increase as the support forces in the brakes increase. Overall, the greater the support forces in the brakes, the more the brakes act to slow the wheels and more strongly the pavement must respond to keep the wheels rotating. The pavement's static frictional forces on the car increase and the car decelerates more quickly.

A toy top is a disk-shaped object with a sharp point and a thin stem projecting from its bottom and top, respectively. When you twist the stem hard, the top begins to spin rapidly. When you then set the top's point on the ground and let go of it, it continues to spin about a vertical axis for a very long time. What keeps the top spinning?

The top has rotational inertia. Explanation: The top continues to spin because it is approximately free of external torques and the net torque on it is essentially zero. It moves according to Newton's first law of rotational motion, turning at constant angular velocity.

To start a motionless toy top spinning, you twist it. What determines the direction in which the top spins?

The torque you exert on the toy top has a direction and the top undergoes angular acceleration in the direction of the torque you exert on it. Explanation: The torque you exert on the top is what causes it to begin spinning. In accordance to Newton's second law of rotational motion, the top undergoes angular acceleration that is proportional to the torque you exert on it and in the same direction as that torque. Your choice of torques thus determines the direction in which the top spins.

an orange ball and a black ball roll of a level table at the same time and in the same direction. The black ball weighs twice as much as the orange ball, but the orange ball is moving twice as fast as the black ball when they leave the table. When and where do those balls hit the level floor belowe the table?

The two balls hit the floor at the same time, but the orange balls hits further from the table. They have different components of velocity in the downfield direction, so the faster moving orange balls travels father downfield during its travels and hits the ground farther from the table than does the black ball

You throw a priceless porcelain vase straight up and watch as it rises to peak height and then drops safely back into your hands. Fortunately, the vase's owner wasn't watching. What were the vase's velocity and acceleration at the moment it reached peak height? [Do not test your answer experimentally, unless you take full responsibility for any consequences!]

The vase's velocity was zero. The vase's acceleration was the acceleration due to gravity, which is not zero. Explanation: While the vase is above your hands, the only force acting on it is its weight. Throughout its trip, the vase is therefore a falling object and it is accelerating downward at the acceleration due to gravity. At the moment the vase reaches its peak height, however, its velocity is momentarily zero--it has just stopped rising and has not yet begun to descend.

Tower cranes are frequently seen in cities, where they are used to construct tall buildings. In a tower crane, a huge metal beam sits atop a vertical metal tower. The beam extends outward from the tower in two directions and it pivots about the top of the tower. A lifting cable hangs from one end of the beam and heavy weights hang from the other end of the beam. Since the lifting cable end of the beam is the only end that seems to do anything, what useful purpose does the weight-end of the beam serve?

The weight-end of the beam ensures that the beam is approximately balanced about its pivot and experiences approximately zero torque due to gravity. Explanation: To be safe and to avoid tipping in unwanted ways, the tower crane must balance its beam about the pivot at the top of its tower. If the beam is seriously unbalanced, meaning that it is experiencing a large gravitational torque about that pivot, it may undergo angular acceleration and thereby start to tip over. The tower itself can exert torques on the beam and compensate for a modest imbalance in the beam. But having the beam extend only in one direction from the pivot and lifting heavy objects from the end of that beam would result in large gravitational torques on the beam about its pivot. To balance the beam and avoid those large gravitational torques, the tower crane extends the beam in both directions and places enough weight near the second end to compensate for weight lifted by the cable near the first end. Gravitational forces acting at the two ends of the beam produce opposing torques that sum to approximately zero and leave the beam nearly free of gravitational torque about the pivot.

Arm-wrestling is a simple game that two people can play. The players sit across from one another at a table, place their right elbows together on the tabletop and clasp their right hands together. When the competition starts, each person tries to twist the pair of arms counterclockwise from that person's perspective until those arms touch the table. It's a rotational problem, with the elbows acting as the pivot and the two players trying to rotate the pair of arms in opposite directions. Suppose you are arm-wrestling with a friend and you are winning. Compare the torque you are exerting on your friend to the torque that your friend is exerting on you.

Those two torques are equal in amount but opposite in direction. Explanation: The torques that you and your friend exert on one another form a Newton's third law pair. The torque you exert on your friend and the torque your friend exerts on you must be equal in amount but opposite in direction, no matter what is happening in the game. The fact that you are winning is irrelevant.

A modern bicycle has two pedals mounted on a rotating device known as a crank. Pushing down on one pedal with your foot produces a torque on the crank, about its pivot, except in which situation(s)?

When the pedal is vertically above or below the pivot, your force on the pedal is directed along the lever arm from the pivot to your force. A force that is parallel to the lever arm produces zero torque. Explanation: If you are able to exert a force on the pedal and that force has a component perpendicular to the lever arm from the pivot to the pedal, you will produce a torque on the crank. There are two orientations of the crank in which those requirements are not met. When the pedal is vertically above or below the pivot, the lever arm from the pivot to the pedal is vertical and a force exerted vertically down on that pedal has zero component perpendicular to the vertical lever arm. This observation that you can't produce a torque on the crank when the pedals are aligned vertically explains why it's so difficult to start riding a bicycle when its pedals are arrange that way.

As a ball bounces on the floor, the floor exerts an upward support force on the ball. Can the amount of that upward support force on the ball be different from the ball's weight?

Yes. It can be greater than the ball's weight and it can be less than the ball's weight. Explanation: The floor's support force on the ball can take any value, depending on how far the ball and floor are denting into one another. During the bounce, the support force starts small and increases as the ball dents deeper into the floor. Eventually, the support force exceeds the ball's weight and the ball begins to accelerate upward. That upward acceleration is crucial to stopping the ball's descent and redirecting its motion upward. As the ball rebounds upward, the support force gradually decreases and eventually becomes zero as the ball leaves the floor's surface.

You are trying to lift a heavy file cabinet into the back of a truck. The file cabinet weighs 200 pounds (about 900 newtons) and you must raise it 2 feet (about 0.6 meters) upward. The file cabinet has wheels, so it rolls freely. You create a ramp using rigid boards that are 8 feet long and successfully push the wheeled file cabinet up the ramp and into the truck. What force did you exert on the file cabinet to keep it moving up the ramp at constant velocity? [Assume the ramp was smooth, straight, and exactly 8 feet long, and neglect any imperfections, such as friction or air resistance.]

You exerted a force of 50 pounds directed uphill along the ramp. Explanation: The work you do lifting the file cabinet into the truck is equal to the increase in the file cabinet's gravitational potential energy. Regardless of how you do that lifting, you will have to do work equal to 200 pounds times 2 feet, or 400 foot-pounds. [The foot-pound is a unit of energy and 1 foot-pound is equal to about 1.36 newton-meters or 1.36 joules.] Lifting the file cabinet straight up at constant velocity would require you to exert an upward force of 200 pounds while that cabinet moves upward 2 feet. But pushing the file cabinet uphill at constant velocity along the 8-foot ramp required you to exert an uphill force of 50 pounds while that cabinet moved uphill 8 feet. The product of your force on the file cabinet times the distance the file cabinet moved in the direction of your force is 400 foot-pounds, either way.

You talking on your cellphone and you accidentally ride your bicycle off the road. You realize that you are going to collide with either a tree or a garbage can, so you must choose which object to hit. The tree will not move at all if you hit the tree, but the garbage can will move if you hit the garbage can. How will your choice of object affect the energy you transfer to that object when you hit it? [Fortunately, you are going slowly, so you won't be injured regardless of your choice.]

You will transfer energy if you hit the garbage can, but you will not transfer energy if you hit the tree. Explanation: Because the tree cannot move, you cannot do work on it and therefore cannot transfer energy to it. You will retain all of your original energy when you hit the tree, which is one of the reasons why hitting immovable objects is often a poor choice during a collision. Giving away excess energy is usually helpful during a collision because uncontrolled energy can lead to injuries. Since the garbage can will move when you hit it, you can do work on the garbage can and transfer energy to it. That's probably your safer choice.

which of the following skaters must be moving at a constant velocity

a skater who is experiencing zero force: to move a constant velocity, skater must be experiencing zero force

*** at what point on a collestion of ramps does a motionless wagon have the mos energy

at the top of tallest ramp

A "lazy susan" is a disk-shaped rotating platform that a restaurant places at the center of a large dining table. Dishes of food are placed on the lazy susan and diners can rotate the lazy susan by hand to bring various dishes closer to them. A large torque exerted for a short time makes the motionless platform begin rotating rapidly, but that dangerous technique risks tipping over some of the food dishes. How can you make the same motionless platform and dishes begin rotating just as rapidly, but with a smaller, safer torque?

do the same angular impulse as the dangerous technique, but by exerting a smaller torque for a longer time. You need to do the same angular impulse as the dangerous technique since it is the same as before and you want to make it spin just as fast. that means that the product of your torque and the time of that torque must be the same as for the dangerous technique. By using a smaller torque, exerted for a longer time, you can obtain that same angular impulse but without the abrupt and risky angular acceleration of the dangerous technique. IT will experience a slower angular acceleration and all the dishes will remain in place.

When you drive a car on a level (horizontal) road that is slippery with ice, you usually have no problems except when you try to speed up, slow down, or turn. Why does the icy road make those three actions hazardous? [neglect any effects due to air]

each action involves a horizontal acceleration and requires a horizontal force. The only forces that level pavement can exert on the car are frictional forces and the slippery ice reduces those frictional forces. A car that is moving at constant velocity on level pavement is inertial and needs no horizontal forces, therefore has no need for frictional forces from the pavement. But when it is accelerating (speeding, slowing up or turning) it is accelerating horizontally and needs a horizontal force. Level pavement can exert vertical support forces and horizontal frictional forces, so those three actions require that the pavement exert horizontal frictional forces on your car. It's those frictional forces that become difficult to obtain when the pavement is icy. Static friction decreases a lot on ice and sliding decreases dramatically on ice, though not all the way to 0. To stay safe, minimize your horizontal accelerations and try to keep your wheels rolling properly so that they experience the stronger static friction rather than the weaker sliding friction.

A meteor is streaking toward city hall and will hit the building in a few second. As it moves through the sky, what physical quantities is the meteor carrying with it? [Ignore any effects due to air or Earth's gravity]

energy, momentum directed toward the city hall, but no force. The meteor carries several conserved quantities with it, including energy and momentum, but it cannot carry force with it. Forces are not conserved quantities and are exerted between objects rather than carried by them. The fact that the meteor is carrying an enormous amount of momentum directed toward city hall means that when it actually hits city hall, the meteor will exert a large impact force on city hall as it transfers some of its momentum to city hall by way of an impulse.

You have a midnight craving for ice cream and are walking quickly through your pitch-black apartment when you collide with the wall. You come to a complete stop. Fortunately, your interior decorator mounted a thick woolen tapestry (wall-hanging) on the concrete wall and that soft tapestry saves you from injury. Compare the momentum you transferred while coming to a stop on the tapestry-covered wall to the momentum you would have transferred if you had come to a stop on the bare concrete wall.

you would have transferred the same momentum in either case, in stopping on the tapestry covered wall you transferred that momentum with a smaller force over a longer period of time. Since momentum is conserved, the momentum you transfer to the tapestry or wall must be equal to your change in momentum. Since your change in momentum is the same in either case (you come to a stop) the momentum you transfer to the tapestry is the same as the momentum you would have transferred to the bare wall. You do the same impulse on either the tapestry or wall, while stopping on the soft tapestry you did the impulse by exerting a relatively large force on the wall for a short time. The concrete wall would have exerted an equal but oppositely directed force on you during the impact and it would have hurt. The tapestry prolonged the momentum transfer and resulted in a more gentle, less painful force.

You are using a string to lift a heavy picnic basket up to your treehouse. Alas, the string isn't strong enough for the job. The picnic basket becomes motionless, even though you are moving the portion of string you are holding upward, and the string breaks. Breaking the string required energy and that energy was provided by:

you. Explanation: Energy is provided to the string by doing work on it. Since you pulled the portion of the string in your hand upward and that portion of string moved upward, you did work on it and provided the string with energy. The picnic basket pulled downward on the portion of string it touched, but that portion of string, like the picnic basket itself, was motionless. Therefore, the picnic basket did no work on the string and gave it zero energy.

You are riding your bicycle forward on a level road, traveling in a straight line at a steady pace. An animal suddenly runs in front of you, so you apply the brakes quickly and stop just in time to avoid hitting the animal. While the brakes are on and you are experiencing a large net force, what is the direction of velocity and acceleration, respectively?

your velocity is forward but your acceleration is backward

You are dragging a heavy chair across the floor and that chair is moving toward the east at constant velocity. The net force on the chair __________________.

zero