Physics Exam 1, Ch1-2 (EOC ex's, slides, CQ's, HWK)
S2.1-Force & lever arm both contribute to torque 1. ______ children produce more torque 2. Sitting close to the pivot ______ torque
1. heavier 2. reduces
Which does more work in lifting a grain of rice over its head: an ant or a person?
A person does more work. Movements that appear large compared to the ant's height still involve small distances and little work.
an object experiences a net force of 40N and has an acceleration of 4m/s^2. The object's mass must be
F=ma 10kg=mass
Newton's 2nd Law of Linear motion
FORCE = mass * acceleration F = m * a
Why can't an acrobat stop himself from spinning while he is in midair?
His angular momentum is conserved.
A child throws a ball perfectly horizontally @ the same time a dirt clod falls off it @ the same height above the ground. The clod falls vertically downward. The time when the clod hits the ground will
be equal to the time the ball hits the ground (Regardless of their horizontal components of velocity, all objects fall at the same rate)
CQ2.3.10 The total kinetic energy of a baseball thrown with a spinning motion is a function of?
both linear and rotational velocities
Linear momentum is conserved as long as there is no outside _____
force
Velocity of an object is =
rate of change of its position
rotational work =
torque * angle (in radians)
Wheels allow static friction to exert _______ on wheels and ______ on vehicle
torques; forces
CQ1.3.4- The work that you do is zero for which of these activities a. carrying your book pack across campus b. throwing a baseball c. lifting a weight up d. pushing a car
a
CQ2.3.8: A competitive diver leaves the diving board and falls toward the water with her body straight and rotating slowly. She pulls her arms and legs into a tight tuck position. Her angular speed a. increases b. decreases c. stays the same d. is impossible to determine
a
If you put your bathroom scale on a ramp and stand on it, will the weight it reports be high, low, or correct?
Low
While you're weighing yourself on a bathroom scale, you reach out and push downward on a nearby table. Is the weight reported by the scale high, low, or correct?
Low
Angular impulse =
Torque · Time
weight =
mass * acceleration due to gravity m * g
R1.12-The Earth moves about the Sun in an elliptical orbit. As the Earth moves closer to the Sun, then which of the following best describes the Earth-Sun system's rotational mass
decrease
Driving down the road, you hit an insect. How does the force your car exerts on the insect compare to the force the insect exerts on the car?
the 2 forces are equal in magnitude
Friction does NOT depend upon:
the area of contact
An unseatbelted driver can be injured by the steering wheel during a head-on collision. The driver hits the steering wheel when the car suddenly comes to a stop bc
the drivers head has inertia.
It's much easier to carry a weight in your hand when your arm is at your side than it is when your arm is pointing straight out in front of you. Use the concept of torque to explain this effect. When your arm is at your side
the force is parallel to the lever arm, not perpendicular.
As you begin pedaling your bicycle and it accelerates forward, the forward force that the bicycle needs to accelerate is exerted by
the ground on the tires
H-when building soap box cars which race by coasting downhill it is better to have solid wheels rather than ones of equal mass with spokes because
the solid wheels have a lower rotational mass & therefore accelerate faster
Suppose you push horizontally on the wall of a building. For you to do positive work on the wall-
the wall moves away from you
Tapping your toothbrush on the sink dries it off because
the water on the toothbrush has inertia.
process of making things happen (process of transferring energy).
work "If you're not pushing or it's not moving, then you are not working." (scalar) W = F * d, where F & d are on the same axis W=Fh=mgh
H- you push on a box w/ a horizontal force of 20N & the box moves a distance of 8m. The amount of work you have done is
work = force * distance = 20 * 8 = 160 J
H-Consider a 100kg father and his 20kg girl. They decide to enjoy balancing a seesaw, which is a uniform board 4m long and pivoted exactly at its center. If the girl sits at the seesaws end (2m from the center), how far from the center on the other side should the father sit?
work = force x distance 40 = 2 x 20 .4m = 100/40
CQ1.3.2 Can a ball ever push downward on a table w/ a force greater than the ball's own weight?
yes
S- Can a ball ever push downward more than its weight?
yes
Your weight and mass are different in that
your weight depends upon local gravity but your mass does not
angular speed
(scalar) change in angle w/ time:
Power =
(work) energy converted/time taken def: how quickly work is done on an object; rate of doing work; w/ more power, more work can be done (& more energy transferred) in the same amnt of time measured in: Watts
7 Forms of Potential Energy
- Chemical - Elastic - Magnetic - Electric - Electrochemical - Nuclear - Gravitational
A sprinter who is running a 200-m race travels the second 100 m in much less time than the first 100 m. Why?
-The sprinter must overcome inertia and accelerate during the first 100 m. During the second 100 m, the sprinter must simply maintain full speed. - Part of the first 100 m is traveled at less than full speed as the sprinter struggles to accelerate from rest.
A ball hits a wall going 10 m/s, and bounces off going 7 m/s. The coefficient of restitution is
.70
Force and distance traveled are at right angles, then work =
0
The value of the average velocity for any round trip is equal to
0
A metro train is traveling at a constant velocity. What are the net forces on (a) the first car, (b) the middle car, (c) and the last car?
0, 0, 0
A 3 bladed wind turbine is rotating with a constant angular velocity of 50radians/s and has a mass of 100kg x M^2. What is the net torque of the turbine?
0N-m
R1.19: If a two-body collision is not head-on, then which of the following may always be assumed? 1. momentum is conserved 2. kinetic energy is conserved 3. neither momentum nor kinetic energy are conserved 4. both momentum and kinetic energy are conserved
1
frictional force 1. opposes __________________ of 2 surfaces -Runs in the direction opposite of the object's________. 2. points along the surfaces 3. acts to bring the two surfaces to one _______
1. relative motion; velocity 3. velocity
When riders move away from pivot, 1. the _____ increases in proportion to lever arm 2. the rotational mass in proportion to _________ 3. Angular _______ decrease! 4. Motions are slower!
1. torque 2. lever arm^2 3. accelerations
S2.1-A balanced seesaw: 1. experiences _____________ 2. moves at _______________________ 3. requires all the individual torques to cancel
1. zero net torque 2. constant angular velocity
A frog leaps straight up with a velocity of 4.9m/s. What is the maximum height reached?
1.2m
E2-A 10-m long elastic band is used to launch a toy glider. Once stretched to a length of 30 m, the band releases 1 J of elastic potential energy when you let it contract 0.1 m. What forward force is the band exerting on the toy glider?
10 N.
E2-A tricycle releases 50 J of gravitational potential energy while rolling 0.5 m directly downhill along a ramp. What is the downhill force acting on the tricycle?
100 N.
A tricycle releases 500J on GPE while rolling down a 5m ramp. What is the weight of the tricycle?
100N
Auto tires are usually hollow and filled with air. If they were solid rubber, their rotational masses would be twice as large. With the wheel lifted, how much rotational torque would it have to exert on a solid tire to undergo the same rotational acceleration?
10x
you operate a 120W lightbulb for 1sec, how much energy did you use?
120J
A frog leaps straight up with an initial velocity of 4.9m/s. How long is the frog in the air?
1s
R1.8: Which of the following is NOT a potential energy? 1. elastic 2. friction 3. chemical 4. nuclear
2
HW: driving down the road, you hit an insect. how does the force your car exerts on the insect compare to the force the insect exerts on the car?
2 forces are equal in magnitude
An 800kg car moving @ 1 m/sec to the right strikes a 400kg car moving to the left. if the cars stick together & stop moving right after the collision, what was the velocity of the 400kg car?
2 m/sec to the left
A gymnast jumps upward with an initial speed of 10m/s. (Assume that g=10m/s^2). She is in the air for a total time of
2 seconds
Rider's part of rotational mass is proportional to 1. the rider's mass 2. ____________________
2. the square of lever arm
E2-A highly compressed spring releases 2 J of elastic potential energy when allowed to expand 1 mm, a small fraction of its overall compression. How much force is the spring exerting on its end?
2000 N.
E2-An elevator releases 10000 J of gravitational potential energy while descending 5 m between floors. How much does the elevator weigh?
2000 N.
The engine on a train has broken down, but it continues to roll forward. It has a mass of 20,000kg and is rolling at 10m/s. To stop it, you grab on and drag your heels, applying a backward force of 100N. How long does it take you to stop the train. It will help to calculate momentum first.
2000s
Suppose you do 1000J of work on a 5kg object, and all the work went into lifting it above the ground. How high above the ground will the object be when all the work has been done?
20m
E2-Your car is broken, so you're pushing it. If your car has a mass of 800 kg, how much momentum does it have when it's moving forward at 3 m/s (11 km/h)?
2400 kg·m/s forward.
R1.15: An object with large momentum 1. requires a lot of force to stop. 2. requires a lot of time to stop. 3. either A or B. 4. none of the above.
3
R1.16: To stop an object 1. in a short time (delta)t requires a large force. 2. with a small force F requires a long time. 3. either of the above. 4. none of the above.
3
E2-When your car is moving at 3 m/s (m=800 kg; f=200N), how much translational kinetic energy does it have?
3600 J.
R:7 A bowler lifts a bowling ball from the floor and places it on a rack. If you know the weight of the ball, what else must you know in order to calculate the work she does on the ball? 1. mass of the ball 2. the time required 3. nothing else 4. height of the rack
4
you drop a marble from rest and after 1 sec, its velocity is 9.8 m/s in the downward direction. What was its velocity after 0.5 sec of falling?
4.9 m/s in downward direction (a freely falling object accelerate downward @ a steady rate)
E2-You're at the roller-skating rink with a friend who weighs twice as much as you do. The two of you stand motionless in the middle of the rink so that your combined momentum is zero. You then push on one another and begin to roll apart. If your momentum is then 450 kg·m/s to the left, what is your friend's momentum?
450 kg·m/s to the right.
A 50kg astranaut is hanging out at rest, another 200kg astronaut zooms by with a velocity of 5m/s and grabs on. What is the velocity of the pair?
4m/s in the direction of the initial astronaut.
HW: what is the potential energy of a 5 kg box that is 6m above ground? (Assume g = 10m/s^2)
5 * 6 * 10 = 300J
The same tricycle begins coasting when it gets to the bottom of the ramp. What is the kinetic energy of the tricycle? What is the speed of the same tricycle?
500J, 10m/s
You walk in a given direction for 20m during the first 5s of a trip and then 15m during the next 2s. Your average speed is equal to
5m/s
What is the angle between the velocity and radius of an object moving in a perfect circle?
90 degrees.
The heads of different golf clubs are angled to give the golf ball different initial velocities. The golf ball's speed remains almost constant, but the angle changes with the different clubs. Neglecting any air effects, how does changing the initial angle of the ball affect the distance the ball travels?
A ball hit horizontally at 45° will travel farthest. A ball hit higher or lower won't travel as far.
E2-An object's center of mass isn't always inside the object, as you can see by spinning it. Where is the center of mass of a boomerang or a horsehoe?
A boomerang or horseshoe's center of mass is in the air between the two arms of the object
Sliding Friction
A force acting to stop surfaces that are already sliding - Forces have fixed magnitudes - weaker horizontal forces - * wastes energy * by converting useful, ordered energy, that can do work, in2 useless thermal energy, a disorder energy. -makes surfaces * hotter * by turning (-) work in2 thermal energy (neg. work = frictional force is in direction opposite of velocity) - Work is done & wear occurs (distance traveled is nonzero)
E2-Why can't you open a door by pushing on its hinged side?
A force exerted at the hinges produces no torque about them. to open the door toque must be applied on it. torque = force * perpendicular distance when the door is pushed at the hinge perpendicular distance is zero. Hence, it can not be opened
E2-How does a bottle opener use mechanical advantage to pry the top of a soda bottle?
A modest force exerted far from the pivot produces an enormous force close to the pivot. Although the opener's handle must travel a long distance, it produces the huge force on the bottle cap that's required to pull that cap off the bottle.
E2-The basket of a wheelbarrow is located in between its wheel and its handles. How does this arrangement make it relatively easy for you to life a heavy load in the basket?
A modest upward force exerted on the handles far from the pivot can balance a large downward weight force exerted on the basket close to the pivot.
Newton's 1st Law of Rotational Motion
A rigid object that's not wobbling and that is free of outside TORQUES rotates at a constant angular velocity.
E2-When you begin to walk forward, what exerts the force that allows you to accelerate?
A static frictional force from the pavement pushes you forward.
Why does distance from the pivot affect speed? - How does lever arm affect torque? - How does lever arm affect rotational mass?
A1: as we remove that force we're changing the lever arm which affects the torque. A2: bigger the lever arm the bigger the torque A3: Farther mass is from the rotation point, the larger the Rotational Inertia • Rotation Mass - Measure of an object's rotational inertia • Distribution of mass changes Rotational Mass -the bigger the rotational mass the more the rotational inertia & the harder it is to start/stop rotating -We can change the rotational mass: the rotational mass is a function of how the mass is distributed about the point of rotation.
E2-When you ride a bicycle, your foot pushes down on a pedal that's 17.5 cm (0.175 m) from the axis of rotation. Your force produces a torque on the crank attached to the pedal. Suppose that you weigh 700 N. If you put all your weight on the pedal while it's directly in front of the crank's axis of rotation, what torque do you exert on the crank?
About 122.5 N·m to the left.
CQ2.3.2: Rank an car dashboard, seatbelt, & airbag in terms of the * impulse * they deliver to a front-seat passenger during a collision, from greatest to least. a. dashboard, seatbelt, airbag b. seatbelt, dashboard, airbag c. airbag, seatbelt, dashboard d. All three are the same.
All three are the same. Bc the passenger is brought from the car's initial speed to a full stop, the change in momentum (equal to the impulse) is the same regardless of what stops the passenger.
What is the Law of Inertia?
An object that is free of external influences moves at a constant velocity (also Newton's 1st Law).
the change in angular velocity w/ time
Angular Acceleration (vector)
E2-While a gymnast is in the air during a leap, which of the following quantities must remain constant for her: velocity, momentum, angular velocity, or angular momentum?
Angular momentum
Suppose you are riding on a merry go round & you move out to the edge. Why does the rotational rate of the system decrease?
Angular momentum is conserved & the rotational mass increased
E2-It's easier to injure your knees and legs while hiking downhill than while hiking uphill. Use the concept of energy to explain this observation.
As you descend, you land hard and your knees and legs must convert your kinetic energy into thermal energy. Injuries can occur.
Consider an elastic ball that is falling downward toward the ground. The ball hits the ground and then begins traveling upward again. At what point in the trip does the ball have the most energy stored in it as elastic potential energy?
At the bottom of the path when it is not moving, right before it rebounds.
When you apply the brakes on your bicycle, which way do you accelerate?
Backward, in the direction opposite your forward velocity.
Wheel hubs still have sliding friction. _______ eliminate sliding friction in wheel hub
Bearings (behave like automatically recycled rollers)
E2-If you sit in a good swivel chair with your feet off the floor, the chair will turn slightly as you move about but will immediately stop moving when you do. Why can't you make the chair spin without touching something?
Because of your rotational inertia (as measured by your rotational mass), you need an external torque in order to begin spinning. While you aren't touching anything in the swivel chair you can't obtain any external torque and can't start spinning.
When you kick a soccer ball, which pushes on the other harder: your foot or the soccer ball?
Both push equally
E2-A jar-opening tool grabs onto a jar's lid and then provides a long handle for you to turn. Why does this handle's length help you open the jar?
By pushing far from the pivot, you exert more torque on the lid.
Describe the motion of a diver performing a rigid, open somersault off a high diving board
COM falls smoothly, obeying the rules governing falling objects. As he falls, his body rotates at a constant angular velocity about his COM. Why? His motion can be separated in2 translational motion of his COM (it falls) & rotational motion about his COM (he rotates about it at a constant angular velocity)
What changes when a ball is dropped?
Changes: Position, time, Velocity "Stays the same/constant:" acceleration (9.8 m/s^2) The velocity is changing linearly with time; the farther the balls falls, the more time it has to accelerate & acquire a large downward velocity & will become v. hard 2 stop. You will have to exert a large upward force to accel. the ball upward & bring it to rest quickly (which wd prolly hurt your hand)......
When your car goes out of control on an icy road, it is safest to use either the clutch or gear shift to allow your car to coast and not be powered by the engine. Why is this so?
Coasting allows the wheels to rotate so as to recover static friction again.
A body whose velocity increases by a constant amount each second has
Constant Acceleration
CQ2.1.9-The wind turbine rotates with constant angular velocity because A. the blades have a very large rotational mass B. the torque from the wind is equal & opposite to the torque from the generator C. the torque from the wind is equal & opposite to the torque from the blades D. the net torque on the blades from the wind is zero
D
CQ2.3.7: If the momentum of an object is tripled, its kinetic energy will change by what factor? a. zero b. one third c. three d. nine
D) momentum = p = m * v 3p = mv^3 KE = 1/2 mv^2 = 1/2 m (3v)^2 = 9 (1/2 mv^2)
no loss of kinetic energy
Elastic collision
capacity to make things happen; ability to do work:
Energy (scalar) Can be transferred by doing WORK. Is conserved. Is measurable measured in = Joules or Newton-meter (N-m) Joule = energy to move an object w/ the force of 1 N over a distance of 1 meter
A horse does work on a cart it's pulling along a straight, level road at a constant speed. The horse is transferring energy to the cart, so why doesn't the cart go faster and faster? Where is the energy going?
Energy is converted to thermal as everything gets warmer.
Newton's 3rd Law of Rotational Motion
For every applied TORQUE, there is an equal and opposite reaction torque. (A result of Newton's 3rd law of linear motion.)
Negative amount of work where the object does work on you:
Force and distance traveled in opposite directions
If you are pulling a sled along a level field at constant velocity, how does the force you are exerting on the sled compare to the force of sliding friction on its runners?
Force exerted is equal to sliding friction
Gravity, support, and friction are all what?
Forces
Suppose you take off in a car with your physics book on top. If you are accelerating forward and the book rides with you, in what direction does friction act on the book?
Forward
When you're driving on a level road and there's ice on the pavement, you hardly notice that ice while you're heading straight at a constant speed. Why is it that you only notice how slippery the road is when you try to turn left or right, or to speed up or slow down?
Friction is only required when attempting to change cars velocity.
CYU2.2.1- Your table @ the restaurant isnt level, & your water glass begins to slide slowly downhill toward the edge. Which way is friction exerting a force on it?
Friction is pushing the glass uphill.
The kicker in a sporting event isn't always concerned with how far downfield the ball travels. Sometimes the balls flight time is more important. If he wants to keep the ball in the air as long as possible, he should kick it at
He should kick the ball straight up. Although the ball will eventually land right where it started, that ball will stay in the air a long time
Conservation of Angular Momentum
If rotational inertia changes, then rotational velocity must change ex: a skater begins a spin w/ arms extended, then moving the arms closer to the body. This motion results in an increase of the speed w/ which the skater rotates. When arms are extended, the moment of inertia of the skater is greater than when the arms are close to the body, since some of the skater's mass decreases the radius of rotation. Bc we can consider the skater an isolated system, with no net external torque acting, when the MOI of the skater decreases, the Angular Velocity increases, according to the equation L = Iσ .
E2-Professional sprinters wear spikes on their shoes to prevent them from sliding on the track at the start of a race. Why is energy wasted whenever a sprinter's foot slides backward along the track?
If the sprinter's foot slides backward, then friction from the ground on the foot does negative work on the foot and extracts energy from the sprinter. That energy becomes thermal energy in the foot and ground.
You're cutting wood with a handsaw. You have to push the saw away from you as it moves away from you and pull the saw toward you as it moves toward you. When are you doing work on the saw?
In both cases, you do work on the saw: when you push it away from you as it moves away from you and as you pull it toward you as it moves toward you. -Whenever you push something in the direction it moves, you do work on it.
kinetic energy is lost -Real collisions are inelastic.
Inelastic collision
A branch falls from a tree with constant acceleration, when does the branch fall the quickest?
It covers more distance in the last second
E2-Some racing cars are designed so that their massive engines are near their geometrical centers. Why does this design make it easier for these cars to turn quickly?
It reduces the car's rotational mass so that the car can undergo rapid angular acceleration and change directions quickly.
E2-You begin pushing the car forward from rest (see Problem 9). Neglecting friction, how long will it take you to push your car up to a speed of 3 m/s on a level surface if you exert a constant force of 200 N on it?
It will take 12 seconds to push the car up to 3 m/s.
E2-A mechanic balances the wheels of your car to make sure that their centers of mass are located exactly at their geometrical centers. Neglecting friction and air resistance, how would an improperly balanced wheel behave if it were rotating all by itself?
It would rotate about its center of mass, not its geometric center. It would appear to wobble as it turned.
You're pushing a child on a swing and exert 50n when pushing away, when returning and pushing back. When is the force the hardest on you?
It's always the same
E2-Some special vehicles have spinning disks (flywheels) to store energy while they roll downhill. They use that stored energy to lift themselves uphill later on. Their flywheels have relatively small rotational masses but spin at enormous angular speeds. How would a flywheel's kinetic energy change if its rotational mass were five times larger but its angular speed were five times smaller?
Its energy would be only 0.2 times as large as before.
3 Forms of Energy: (scalar)
Kinetic, Potential, Thermal
Angular momentum
Linear momentum x Radius = rotational inertia x angular velocity The momentum of an object that is either rotating or in circular motion, and is equal to the product of the moment of inertia and the angular velocity. (why it's hard to stop a spinning carousel)
impulse
Momentum is transferred to a car by giving it an: -The harder and longer you push a bobsled forward at the start of a race, the more momentum it will have when it starts down the hill. -points in the same direction as the force
As you jump across a stream, does a horizontal force keep you moving forward? If so, what is this force?
No, there is no horizontal force. You continue to move forward bc of inertia.
When you lie on a spring mattress, it pushes most strongly on the parts of you that stick into it the farthest. Why doesn't it push up evenly on your entire body?
Obeys Hooke's law
Padded soles in running shoes soften the blow of hitting the pavement. Why does padding reduce the forces involved in bringing your foot to rest?
Padding means greater distortion means the collision lasts longer, and impulse equals force times time.
E2-Why does putting sand in the trunk of a car help to keep the rear wheels from skidding on an icy road?
Pressing the wheels more tightly against the pavement increases the maximum force that static friction can exert on the wheels.
Farther mass is from the rotation point, the larger the _____________
Rotational Inertia
E2-Skiers often stop by turning their skis sideways and skidding them across the snow. How does this trick remove energy from a skier, and what happens to that energy?
Skidding sideways dos work against sliding friction, converting some of the skiers kinetic energy into thermal energy.
E2-Firefighter slide down a pole to get to their trucks quickly. What happens to their gravitational potential energy, and how does it depend on the slipperiness of the pole?
Sliding friction converts some into heat, but a slippery pole converts a considerable fraction into kinetic energy.
When you first let go of a bowling ball, it's not rotating. But as it slides down the alley, it begins to rotate. Use the concept of energy to explain why the ball's forward speed decreases as it begins to spin.
Some of the ball's translational kinetic energy converts into rotational kinetic energy.
A car accelerated from rest forwards what frictional force does the ground do on the wheels?
Static frictional force forwards.
A horse begins pulling a cart from rest. What work does the ground do on the wheels?
Static frictional force that points backwards.
Newton's 2nd Law of Rotational Motion
TORQUE = Rotational Mass * Angular Acceleration -The angular acceleration points in the same direction as the torque (T = I α , which looks like F = ma )
An acorn falls from a branch located at 9.8m above the ground. After 1s of falling, the acorns velocity will be 9.8m/s downward. Why hasn't the acorn hit the ground?
The acorns average speed for the 1s is less than 9.8m/s.
E2-The chairs in an auditorium aren't all facing the same direction. How could you describe their angular positions in terms of a reference orientation and a rotation?
The angle by which the front, center seat would have to be rotated, as viewed from above, to have each seat's orientation.
E2-Describe the process of writing with chalk on a blackboard in terms of friction and wear.
The chalk experiences sliding friction as your write and leaves visible wear chips on the blackboard.
E2-A common pair of pliers has a place for cutting wires, bolts, or nails. Why is it so important that this cutter be located very near the pliers' pivot?
The closer the wire is to the axis of pliers' axis of rotation, the less effective any force from the wire is at producing a torque on the pliers and stopping its rotation.
E2-When a star runs out of nuclear fuel, gravity may crush it into a neutron start about 20 km (12 miles) in diameter. While the star may have taken a year or so to rotate once before its collapse, the neutron star rotates several times a second. Explain this dramatic increase in angular velocity.
The collapsing star's angular momentum can't change. Since its rotational mass decreases, its angular velocity must increase.
A wooden block comes to a stop on a wooden desk. What work is done on the objects involved?
The desk does negative work on the block.
A dolphin can leap several meters above the ocean's surface. Why doesn't gravity stop the dolphin from leaving the water?
The dolphin's inertia carries it upward, even though its weight makes it accelerate downward & gradually stop rising.
The best running tracks have firm but elastic rubber surfaces. How does a lively surface assist a runner?
The energy of the collisions between the runner's feet and the track surface is largely not lost, but returned to the runner.
E2-When you climb out on a thin tree limb, there's a chance that the limb will break off near the trunk. Why is this disaster most likely to occur when you're as far out on the limb as possible?
The farther out the limb that your weight is exerted on the branch, the larger the torque you produce on the limb and the more likely it is to begin rotating.
E2- A gristmill is powered by falling water, which pours into buckets on the outer edge of a giant wheel. The weight of the water turns the wheel. Why is it important that those buckets be on the wheel's outer edge?
The farther the water is from the water wheel's pivot, the more torque its weight produces on the wheel.
If you drop a steel marble on a wooden floor, why does the floor receive most of the collision energy and contribute most of the rebound energy?
The floor is softer and more massive than the marble
E2-What is the momentum of a fly if it's traveling 1 m/s and has a mass of 0.0001 kg?
The fly's momentum is 0.0001 kg-m/s.
Why can't you open a door by pushing its doorknob directly toward or away from its hinges?
The force is parallel to the lever arm, not perpendicular.
E2-As you begin pedaling your bicycle and it accelerates forward, what is exerting the forward force that the bicycle needs to accelerate?
The ground exerts a forward frictional force on the bicycle wheels.
Relationship of impulse & momentum:
The impulse due to all forces acting on an object (the net force) is equal to the change in momentum of the object. impulse = m x change in V = F x change in t Rem: impulse, like momentum, is a vector quantity, it points in the same direction as the force. ie: the more force or the longer that force is exerted, the larger the impulse & the more your bumper car's momentum changes. impulse = * F * x t = F x * t *
E2-When you push down on the handle of a doll-like wooden nutcracker, its jaw pivots upward and cracks a nut. If the point at which you push down on the handle is five times as far from the pivot as the point at which the jaw pushes on the nut, how much force will the jaw exert on the nut if you exert a force of 20 N on the handle? (Assume all forces are at right angles to the lever arms involved.)
The jaw will exert a force of 100 N on the nut.
E2-A yo-yo is a spool-shaped toy that spins on a string. In a sophisticated yo-yo, the end of the string forms a loop around the yo-yo's central rod so that the yo-yo can spin almost freely at the end of the string. Why does the yo-yo spin longest if the central rod is ver thing and very slippery?
The nearer the frictional force is to the pivot, the less torque it produces to slow the yo-yo's rotation. Slipperiness reduces friction.
E2-Tightrope walkers often use long poles for balance. Although the poles don't weigh much, they can exert substantial torques on the walkers to keep them from tipping and falling off the ropes. Why are the poles so long?
The longer the pole is, the greater its rotational mass and the more torque that is required to start it rotating significantly. When the pole has a large rotational mass, the tightrope walker can exert large torques on the pole without causing it to rotate quickly. The pole twists back on the tightrope walker and helps the tightrope walker remain upright.
E2-An electric saw uses a circular spinning blade to slice through wood. When you start the saw, the motor needs 2 seconds of constant angular acceleration to bring the blade to its full angular velocity. If you change the blade so that the rotating portion of the saw now has three times its original rotational mass, how long will the motor need to bring the blade to its full angular velocity?
The motor will need 6 seconds of constant acceleration to bring the new blade up to full angular velocity. With 3 times the rotational mas, the angular acceleration of the new blade is only 1/3 of what it was originally.
If you pull slowly on the top sheet of a pad of paper, the whole pad will move. But if you yank suddenly on that sheet, it will tear away from the pad. What causes these different behaviors?
The pad's inertia tends to keep it in place. If you pull the paper away too quickly, the pad won't be able to accelerate with the paper.
E2-Explain why a rolling pin flattens a piecrust without encountering very much sliding friction as it moves.
The pin's surface turns with the crust and doesn't slide across it.
E2-When an airplane starts its propellers, they spin slowly at first and gradually pick up speed. Why does it take so long for them to reach their full rotational speed?
The propellers have rotational inertia (as measured by their moments of inertia). The propellers must undergo angular acceleration and only gradually speed up to their full rotational speeds.
To weigh an infant you can step on a scale once with the infant and then again without the infant. Why is the difference between the scale's two readings equal to the weight of the infant?
The scale responds to the downward force exerted on it
A ball falls from rest for 5 seconds. Neglecting air resistance, during which of the 5 seconds does the ball's speed increase most?
The speed change is the same during each of the 5 seconds.
E2-An antique carousel that's powered by a large electric motor undergoes constant angular acceleration from rest to full rotational speed in 5 seconds. When the ride ends, a brake causes it to decelerate steadily from full rotational speed to rest in 10 seconds. Compare the torque that starts the carousel to the torque that stops it.
The starting torque must be twice a large as the stopping torque and the two torques must be in opposite directions.
E2-How does the string of a yo-yo get the yo-yo spinning?
The string pulls on the outside edge of the yo-yo's spindle and at right angles to the lever arm between the yo-you's rotational axis and the point at which the force acts. As a result, it produces a torque on the yo-you about its rotational axis and causes the yo-yo to undergo angular acceleration.
A toy top spins for a very long time on its sharp point. Why does it take so long for friction to slow the top's rotation?
The tip is small, so the frictional torque is small too.
explain projectile motion
The trajectory is an arc bc the velocity of the ball is not constant. Vertical motion is accelerated due to gravity, whereas horizontal velocity is constant due to lack of horizontal forces 2 components of motion = horizontal & vertical that are independent of eachother
E2-You can do push-ups with either your toes or your knees acting as the pivot about which your body rotates. When you pivot about your knees, your feet actually help you to lift your head and chest. Explain.
The weights of your chest and your feet exert torques in opposite directions about your knees. They partially balance one another.
E2-Why is it hard to start the wheel of a roulette table spinning, and what keeps it spinning once it's started?
The wheel has rotational inertia, as measured by its rotational mass, making it hard to start and stop spinning
E2-A horse does work on a cart it's pulling along a straight, level road at a constant speed. The horse is transferring energy to the car, so why doesn't the cart go faster and faster? Where is the energy going?
The work that the horse does on the car is wasted in opposing friction. The work becomes thermal energy.
When an airplane starts its propellers, they spin slowly at first and gradually pick up speed. Why does it take so long for them to reach their full rotational speed?
They have a large rotational mass.
E2-When you start your computer, the hard disk begins to spin. It takes 6 seconds of constant angular acceleration to reach full speed, at which time the computer can begin to access it. If you wanted the disk drive to reach full speed in only 2 seconds, how much more torque would the disk drive's motor have to exert on it during the starting process?
Three times as much torque.
E2-In countless movie and television scenes, the hero punches a brawny villain who doesn't even flinch at the impact. Why is the immovable villain a Hollywood fantasy?
To avoid accelerating when pushed on with a force, the villain would have to have infinite mass. That's impossible.
Static Friction
When nothing is sliding; acts 2 prevents objects 4m starting to slide. - Force is limited: can vary from 0 --> upper limit -enables objects to do work on one another -provides greater traction - * No work * is done & no wear occurs (distance traveled is zero)
E2-When you first let go of a bowling ball, it's not rotating. but as it slides down the alley, it begins to rotate. Use the concept of energy to explain why the ball's forward speed decreases as it begins to spin.
When the bowling ball is rotating, it has rotational kinetic energy. That energy must come from somewhere and since the only type of energy the ball has as it first begins to slide down the lane is translational kinetic energy, the rotational energy must come from the translational kinetic energy. As a result, the translational kinetic energy must decrease, so the ball must slow down.
E2-Falling into a leaf pile is much more comfortable than faling onto the bare ground. In both cases you come to a complete stop, so why does the leaf pile feel so much better?
When you land on a leaf pile, a modest upward force exert for a long time stops you. When you land on bare ground, large upward force exerted for a small time stops you. Obviously, the modest force is more comfortable than the large force.
E2-It's must easier to carry a weight in your hand when your arm is at your side than it is when your arm is pointing straight out in front of you. Use the concept of torque to explain this effect.
When your arm is pointing straight out in front of you, any weight force exerted on your is at right angles to the lever arm between your shoulder and hand and produces a large torque about your shoulder. On the other hand, when your arm is at your side, any weight force exerted on your hand is directed away from your shoulder and produces no torque about your shoulder.
CQ1.3.5-If you push on a friend, will that friend always push back on you?
Yes
While hanging a picture, you accidentally dent the wall with a hammer. Did the hammer do work on the wall?
Yes, it pushed the wall inward and the wall dented inward
Are you doing work while kneading bread? If so, when?
Yes, you are doing work whenever you push on the bread and it moves in the direction of that push.
When you fly a kite, there is a time when you must do (+) work on the kite. Is that time when you let the kite out or when you pull it in?
You do (+) work when you pull the kite in. -When you pull the kite in you pull toward you & the kite moves toward you, so you do work on the kite
E2-One way to crack open a walnut is to put it in the hinged side of a door and then begin to close the door. Why does a small force on the door produce a large force on the shell?
Your force far from the hinges produces a large torque. To oppose this torque, the nut must exert a huge force near the hinges.
E2-How does a crowbar make it easier to lift the edge of a heavy box a few centimeters off the ground?
Your small effort exerted on the crowbar far from its pivot produces a large force on the box, located near the crowbar's pivot.
R1.3: You are pushing a file cabinet across the floor in a straight line at a steady speed. Which of the following statements is correct? a. The magnitude of the force that you're exerting on the file cabinet must be more than the magnitude of its weight. b. The magnitude of the force that you're exerting on the file cabinet must be equal to the magnitude of the force that friction is exerting on it. c. The magnitude of the force that you're exerting on the file cabinet must be more than the magnitude of the force that friction is exerting on it.
a
To improve efficiency of wind turbines...which natural phenomena was used....
a school of fish
CQ2.2.2:A car and a semi-truck, both equipped w/ tires made of the same material, skid on the same road. Which experiences the greatest force from friction? a. The truck. b. The car. c. Both have the same frictional force. d. Need more information.
a) the truck bc its more massive
CQ2.3.3: Rank an automobile dashboard, seatbelt, & airbag in terms of the * avg force * they deliver to a front-seat passenger during a collision, from greatest to least. a. dashboard, seatbelt, airbag b. seatbelt, dashboard, airbag c. airbag, seatbelt, dashboard d. All three are the same.
a. dashboard, seatbelt, airbag The dashboard stops the passenger very quickly in a front-end collision, resulting in a very large force. The seatbelt takes somewhat more time, so the force is smaller. Used along with the seatbelt, the airbag can extend the passenger's stopping time further, notably for his head, which would otherwise snap forward.
CQ2.3.11 To stop an object a. in a short time t requires a large force. b. with a small force F requires a long time. c. either of the above. d. none of the above
a. in a short time t requires a large force.
CQ1.2.2 Gravity causes objects to ________ downward
accelerate. all objects fall at the same rate regardless of their mass; however more massive ones experience greater forces. When falling objects pick up speed and this is called acceleration due to gravity.
S1-Net FORCE determines object's ____________.
acceleration
change in velocity
acceleration (ANY change in your velocity=speeding up, slowing down, or turning)
You are calculating a problem and know the answer must have units of velocity and are searching for a possible formula. Which formulae would work for the problem?
acceleration X time
The earth exerts a downward force of 850 N on a veteran astronaut as he works outside the space shuttle. What force (if any) does the astronaut exert on the earth?
an upward force of 850 N on the earth.
S2-Net TORQUE determines object's___________________
angular acceleration
A spinning car carries _________________ - A conserved quantity (can't create or destroy) - Measures difficulty reaching angular velocity
angular momentum - V
an object's orientation relative to the axis. (points along rotation axis)
angular position (vector)
A baseball player balances a bat on his finger; the bat is laying sideways and not standing on end. The bat will balance
at its center of mass.
List objects in order from largest to smallest?
atom, nucleus, proton, quark
CQ2.2.1:A crate is located in the center of a flatbed truck. The truck accelerates to the east, & the crate moves w/ it, not sliding at all. What is the direction of the friction force exerted by the truck on the crate? a. to the west b. to the east c. No friction force exists because the crate is not sliding
b
CQ2.3.6: Consider a playground merry-go-round. A child is standing on the outside edge of the spinning merry-go-round. Then, the child moves closer to the center. What changes when the child moves to the center of the merry-go-round? L=angular momentum, W=angular velocity, I= rotational mass a. L increases, w decreases and the I stays the same b. L stays the same, w increases and the I decreases c. L decreases, w decreases and the I decreases d. L increases, w increases and the I decreases e. L stays the same, w decreases and the I increases
b
CQ2.3.9: A figure skater with arms initially extended starts spinning on the ice at 3 rad/s. After she then pulls her arms into her body, which of the following results? a. a smaller rotational rate b. a greater rotational rate c. a greater angular momentum d. a smaller angular momentum
b
S-A ramp makes lifting a box easier because... a. You can use less energy to lift the box b. The ramp exerts some force on the box c. A ramp lets you use wheels
b
CQ2.1.1- You and a child half your height lean out over the edge of a pool at the same angle. If you both let go simultaneously, who will tip over faster and hit the water first? a. You hit the water first b. Child hits the water first c. Both hit at the same time
b (you have a larger rotational inertia than the child bc your mass is further from the point of rotation, making it harder to rotate)
CQ2.3.12 If a two-body collision is not head-on, then which of the following may always be assumed? 1. momentum is conserved 2. kinetic energy is conserved 3. neither momentum nor kinetic energy are conserved 4. both momentum and kinetic energy are conserved
both momentum and kinetic energy is conserved
CQ1.3.3- The work that gravity does is positive when you a. lift a weight up b. push a car forward c. walk downstairs
c
CQ2.2.3:The work done by static friction is always a. positive b. negative c. along the surface d. zero
c
R1.9: Under what conditions is the total angular momentum of a system conserved? a. It is always conserved. b. When there is no net outside force. c. When there is no net outside torque. d. When the kinetic energy is also conserved
c
S-To stop an object a. in a short time (delta)t requires a large force. b. with a small force F requires a long time. c. either of the above.
c
R.5 :A car increases its speed from 30 mph to 60 mph. What happens to its kinetic energy? a. No change b. It increases by a factor of 2. c. It increases by a factor of 4.
c) (Doubling the speed of the car requires quadrupling the energy transferred to it. )
A baseball player throws a bat up in the air, so that it spins as it translates. The bat will rotate about its
center of mass
S2.1-The point about which an object's mass balances
center of mass
acceleration =
change in * velocity * /change it time speeding up, slowing down (deceleration), or turning (vector)
angular speed =
change in angle/time
You jump from a platform and dive gracefully into a pool. At the peak of the jump, your velocity is
changing, but acceleration is constant
S2.1- A balanced seesaw has constant ________________. • It's ____________ is constant when it is - motionless and horizontal - motionless and tilted - turning steadily in any direction
constant angular velocity
A balanced seesaw has:
constant angular velocity Its AV is constant when it's: -motionless & horizontal -motionless & tilted -turning steadily in any direction
For a bullet fired horizontally, the horizontal velocity is:
constant, & independent of its vertical falling motion
3rd law note: While the forces two objects exert on one another must be equal & opposite, the net force on each object can be anything. • Each force within an equal-but-opposite pair is exerted on a ____ object, so ________________
different; they don't cancel directly
speed =
distance/elasped time
rotational inertia
distribution of mass changes rotational inertia. Further mass is 4m the rotation point, the larger the rotational inertia. Ex: diver tuck-in arms & legs in order to concentrate body's mass towards the center, thus creating a faster acceleration.
CYU1.3.2 As you ride upward in an elevator @ a constant velocity, what 2 forces act on your body & what is the net force on you?
downward weight & upward support force from the floor. They balance, so the net force on you is zero.
potential energy
energy stored by an object that can be transformed into another form of energy; energy stored in forces. Ex: H2O behind a dam, chemical energy in food, firecracker, wound clock spring, bowling ball at the top of a hill, cloud in a thunderstorm, uranium
Newton's 3rd Law of linear Motion
equal & opposites
force can produce a torque; torque can produce a force
ex: you put a force at a distance from the pivot it will produce a torque - the torque, in turn, will produce a force when the lever arm hits your fingers
in order to do a (+) amnt of work you must
exert a force & move in the direction of the force
in order to do a positive amount of work, you must
exert a force & move in the direction of the force (you did work on the object)
Impulse is defined as change of momentum. Impulse is also (=) to the avg force for the time the force is applied. thus force and momentum are related in that
force is a change in momentum per unit time
Work is the result of ____ causing _____
force, motion
Suppose you take off in a car w/ your physics book on top. If you are accelerating froward & the book rides w/ you, in what direction does friction act on the book?
forwards
if you are backing-up & slowing-down, your acceleration is directed
forwards?
H- What is the potential energy of a 5kg box that is 6m above the ground? (Assume g=10m/s^2)
gravitational potential energy = mass * acceleration due to gravity * height U = m * g * h = 5 * 10 * 6 = 300 J
R1.6-A solid disk and a hoop have the same mass and radius. Which has the larger rotational inertia about its center of mass?
hoop
Newton's 1st Law of Linear motion
inertia
property of steady motion in the absence of any outside influences:
inertia (scalar)
R1.14 The impulse experienced by a body is equivalent to its change in what quantity?
momentum
Harder to rotate:
more rotational inertia
angular velocity =
its change in angular position with time (vector) 1/s = radian per second
A projectile is thrown directly upward and caught again. At the top of its path
its vertical velocity is 0.
CQ1.2.3 A projectile is thrown directly upward & caught again. At the top of its path
its vertical velocity is zero
An object undergoing free fall experiences:
its weight acceleration downward its velocity becomes increasingly downward (whether going up or down, its still falling) Its * HORIZONTAL * coasting motion is independent of its * VERTICAL * falling motion
A moving wheel has kinetic energy =
kinetic energy = ½ · mass · speed^2
A spinning wheel has kinetic energy =
kinetic energy = ½ · rotational mass · ang. speed^2
Easier to rotate:
less rotational inertia
torque =
lever arm · force (Where the lever arm is perpendicular to the force) measured in = (Nm) a twist or spin (vector) Ex: opening a jar, turning an engine, spinning a toy top, using a wrench, chewing
Force =
m * a measured in = N 1N force will gv a 1kg mass an acceleration of 1m/s^2
momentum =
m * v def: measure of difficulty reaching present velocity - its determination 2 keep moving the way it's currently moving. (ie: your car's momentum indicates the effort it took 2 get the car moving w/ its present speed & direction of motion). To distinguish it 4m energy & angular momentum, you can think of it as the * conserved * quantity of moving. -Same direction as velocity measured in = kg-m/s Note: A moving object carries only momentum, * not force *; a stopped bumper car has a 0 velocity & 0 momentum Impulse= a force exerted for a certain period of time = F x t
an object maintains its state of motion bc it has:
mass
measure of inertia:
mass (doesn't depend on gravity)
gravitational potential energy =
mass x acceleration due to gravity x height U = m x g x h (h=change in potential energy from 0 - ?) or Units = kg x m/s^2 x m = Joule "The higher they were the harder they hit"
resistance of an object to change its velocity. measure of inertia (does not depend on gravity);
mass!!!! (Scalar) Measured in Kg it is independent of the location in the universe. since mass is independent of the force of gravity an astronaut will still have the same mass on the moon!!!
rotational inertia
measure of how difficult it is to get an object to rotate. - Scalar (Objects are harder to rotate if more of their mass is further away from the axis of rotation. It depends upon the mass of the object and the way the mass is distributed.)- A body that's rotating tends to keep rotating
to accelerate you must experience a _______
net force Accel. is inversely proportional to the mass of the object (2nd law). More massive = harder it is to accelerate F = ma
angular acceleration =
net torque/rotational mass
Suppose your car's speed triples. By what factor will its kinetic energy change?
nine times greater
CQ1.2.1: throw a ball into the air, after the ball leaves my hand, is there any force pushing the ball upward?
no
You throw a ball straight up. Ignoring air resistance, after it leaves your hand it will experience
only the downward force of its weight
an object's location relative to x-y coordinates
position (vector)
force? Net Force?
push/pull (vector) Sum of all the individual forces being exerted on you; acceleration depends on the strength of the net force.
Suppose you double the length of the blades of a wind turbine. For the same wind conditions, the torque on the turbine
quadruples
Angular position measured in:
radians
Suppose you are a football player & you kick a ball for a field goal. Ignoring air resistance, the balls horizontal velocity
remains constant throughout the path
used to find the direction of the angular velocity
right-hand rule: fingers curl in direction of rotation & thumb points towards angular velocity
A spinning frisbee is thrown between 2 persons in a park. the motion of the frisbee is
rotational & translational
Wheels eliminate _________ friction
sliding
change in distance traveled w/ time:
speed - S
Accel. in same direction as velocity = Accel. in direction opposite to velocity = Accel. at right angles to velocity =
speed increases speed decreases direction changes
velocity =
speed with a direction measured in = m/s^2 (vector) Ex: 50mph southeast
Free wheels are turned by ______friction
static
Powered wheels use ______ friction to propel car
static
what type of friction causes bearings to not waste much energy?
static
Conservation of momentum =
transferred but not destroyed If the net external force on a system is zero, then the total linear momentum of the system does not change.
R1.1 If the net force on a hot-air balloon is directed straight upward, which way does the acceleration point?
upward
change in position with time
velocity (vector)
measure of the force exerted (on the falling ball) by * gravity * :
weight (vector) Measured in Newtons 1 N = 1 kg-m/s^2 1kg = 10N depends on location in universe. (in space there is no gravity & therefore an astronaut wd be weightless!!!)
A speedboat is pulling a water-skier with a rope, exerting a lg forward force on her. The skier is traveling in a straight line at a constant speed. The net force she experiences is
zero.
you drop a marble from rest and after 1 ses, it has fallen a downward distance of 4.9m. How far had it fallen after 0.5sec?
~1.2m (while a freely falling object's velocity changes steadily in the downward direction, its change in height is more complicated. when you drop the marbel 4m rest, it starts its descent slowly but picks up speed. In the 1st 0.5sec, it travels only 1/4 of the distance it travels in the 1st second, or about 1.2m )
S2.1 explain the Lone Rider's descent on a seesaw
• Rider's weight produces a torque on the seesaw • Seesaw undergoes angular acceleration • Seesaw's angular velocity increases rapidly • Rider's side of seesaw soon hits the ground
