Physics midterm

You are standing on a straight stretch of road and watching the motion of a bicycle; you choose your position as the origin. At one instant, the position of the bicycle is negative and its velocity is positive. Is the bicycle getting closer to you or farther away? Explain.

If the position of the bicycle is negative it is to your left. The bicycle's velocity is positive, or to the right, so the bicycle is getting closer to you

Jonathan accelerates away from a stop sign. His eight-year-old daughter sits in the passenger seat. On whom does the back of the seat exert a greater force?

Jonathan

Does a real automobile have constant acceleration? Measured data for a Porsche 944 Turbo at maximum acceleration are as follows: Based on your graph, is the acceleration constant? Use your graph to estimate the car's acceleration at 2.0 s. Give your answer in SI units. Hint: Remember that acceleration is the slope of the velocity graph. Use your graph to estimate the car's acceleration at 8.0 s. Give your answer in SI units. Hint: Remember that acceleration is the slope of the velocity graph.

No, it decreases with increasing time. 5.1 m/s^2 2.0 m/s^2

Josh and Taylor, standing face-to-face on frictionless ice, push off each other, causing each to slide backward. Josh is much bigger than Taylor. After the push, which of the two is moving faster?

Taylor will be moving faster.

A car travels along a straight east-west road. A coordinate system is established on the road, with x increasing to the east. The car ends up 16 mimi west of the origin, which is defined as the intersection with Mulberry Road. If the car's displacement was -27 mi , what side of Mulberry Road did the car start on? How far from the intersection was the car at the start?

The car started 11 mi east of Mulberry Road.

You are cycling around a circular track at a constant speed. Does the magnitude of your acceleration change? The direction?

The magnitude of the acceleration doesn't change. But the direction does.

If a car stops suddenly, you feel "thrown forward." We'd like to understand what happens to the passengers as a car stops. Imagine yourself sitting on a very slippery bench inside a car. This bench has no friction, no seat back, and there's nothing for you to hold on to. Use Newton's laws to explain why you seem to be "thrown forward" as the car stops. Is there really a force pushing you forward?

The net force on you has remained zero because the net vertical force is zero and there are NO HORIZONTAL FORCES. According to Newton's FIRST law, if the net force on you is zero, then you continue to move in a straight line with a constant velocity. That is what happens to you when the car slows down. You continue to move forward with a constant velocity.

A beach ball is thrown straight up, and some time later it lands on the sand. Is the magnitude of the net force on the ball greatest when it is going up or when it is on the way down? Or is it the same in both cases? Explain. Air resistance should not be neglected for a large, light object.

The only contact force is the FORCE OF AIR DRAG on the ball. The only long-range force is the weight of the ball. Drag always points in the direction OPPOSITE to the motion. Thus the weight of the ball and the drag force always reinforce each other if the ball is moving straight UP. The net force is larger on the way UP.

A student at the top of a building of height hℎ throws ball A straight upward with speed v0 and throws ball B straight downward with the same initial speed. Compare the ball's accelerations, both direction and magnitude, immediately after they leave her hand. Is one acceleration larger than the other? Or are the magnitudes equal? Compare the final speeds of the balls as they reach the ground.

They are equal. They are equal.

If your car is stuck in the mud and you don't have a winch to pull it out, you can use a piece of rope and a tree to do the trick. First, you tie one end of the rope to your car and the other to a tree, then pull as hard as you can on the middle of the rope, as shown in the figure. This technique applies a force to the car much larger than the force that you can apply directly. To see why the car experiences such a large force, look at the forces acting on the center point of the rope, as shown in the figure. The sum of the forces is zero, thus the tension is much greater than the force you apply. It is this tension force that acts on the car and, with luck, pulls it free.(Figure 1) The sum of the three forces acting on the center point of the rope is assumed to be zero because When you are pulling on the rope as shown, what is the approximate direction of the tension force on the tree?

This point is not accelerating. East

shows growth rings in the trunk of a pine tree. You can clearly see the wide and the narrow rings that correspond to years of fast and slow growth. You can think of these rings as a motion diagram for the growth of the tree.

U looking graph

(Figure 1) shows a situation in which the force of the road on the car's tire points forward. In other situations, the force points backward. Give an example of such a situation.

When the car is going forward and slowing down.

An airplane has been directed to fly in a clockwise circle, as seen from above, at constant speed until another plane has landed. When the plane is going north, is it accelerating? When the plane is going north, in what direction does the acceleration vector point?

Yes, it is. Since the plane is moving in a circle and constantly changing direction, at any point along its motion the plane is constantly accelerating. east

A block has acceleration a when pulled by a string. If two identical blocks are glued together and pulled with twice the original force, what will their acceleration be?

a

The gas pedal in a car is sometimes referred to as "the accelerator." Which other controls on the vehicle can be used to produce acceleration?

al of the above

A ball is thrown straight up into the air. At each of the following instants, is the ball's acceleration ay equal to g, -g, 0<g, or >g? Just after leaving your hand? At the very top (maximum height)? Just before hitting the ground?

all 3 is ay = -g

In each of the following segments of the motion, are the cars accelerating, or is their acceleration zero? The cars are accelerating Which way does their acceleration vector point as the cars roll up the ramp? Which way does their acceleration vector point at the highest point on the ramp? Which way does their acceleration vector point as the cars roll back down the ramp?

as the cars roll down the ramp as they roll up the ramp at the highest point on the ramp downward along the ramp down down

Walking without slipping requires a static friction force between your feet (or footwear) and the floor. As described in this chapter, the force on your foot as you push off the floor is forward while the force exerted by your foot on the floor is backward. But what about your other foot, the one moved during a stride? What is the direction of the force on that foot as it comes in contact with the floor?

backward

Give an example of a trip you might take in your car for which the distance traveled as measured on your car's odometer is not equal to the displacement between your initial and final positions.

circular motion with a constant speed Submit

One consequence of Einstein's theory of special relativity is that mass is a form of energy. This mass-energy relationship is perhaps the most famous of all physics equations: E=mc2, where m is mass, c is the speed of the light, and E is the energy. In SI units, the units of speed are m/sm/s. For the preceding equation to have consistent units (the same units on both sides of the equation), the units of E must be which of the following? View Available Hint(s)

kg*m^2/s^2

shows an acceleration-versus-force graph for three objects pulled by rubber bands. The mass of object 2 is 0.40 kg What is the mass of object 1? Mass of object 3? Explain your reasoning.

m1 = 0.16 kg m3 = 1 kg A larger slope implies a smaller mass. We know the mass of object 2, and we can find the other masses relative to m2 by comparing their slopes.

When you blink your eye, the upper lid goes from rest with your eye open to completely covering your eye in a time of 0.024 s. Estimate the distance that the top lid of your eye moves during a blink. What is the acceleration of your eyelid? Assume it to be constant. What is your upper eyelid's final speed as it hits the bottom eyelid?

1 cm 3.5×10m/s^2 0.84 m/s

A girl stands on a sofa. Identify the number of the action/reaction pairs of forces between the girl and the sofa.

1 pair

Weddell seals make holes in sea ice so that they can swim down to forage on the ocean floor below. Measurements for one seal showed that it dived straight down from such an opening, reaching a depth of 0.30 km in a time of 5.0 min. What was the speed of the diving seal?

1.0 m/s

A rectangle has length 3.24 mm and height 0.432 mm .

1.4

The earth formed 4.57×10^9 years ago. What is this time in seconds?

1.44 x 10^17 s

man's higher initial acceleration means that a man can outrun a horse over a very short race. A simple - but plausible - model for a sprint by a man and a horse uses the following assumptions: The man accelerates at 6.0 m/s2m/s2 for 1.8 ss and then runs at a constant speed. A horse accelerates at a more modest 5.0 m/s2m/s2 but continues accelerating for 4.8 ss and then continues at a constant speed. A man and a horse are competing in a 200 mm race. The man is given a 100 mm head start, so he begins 100 mm from the finish line. How much time does the man take to complete the race? How much time does the horse take? Who wins the race?

10 s 11 s man wins

Estimate the average speed, in m/s, with which the hair on your head grows. Make this estimate from your own experience noting, for instance, how often you cut your hair and how much you trim.

10^-8 m/s

A person walks briskly at 2.10 m/s .

12.8 min

A car can go from 0 to 60 mph in 14 s . A second car is capable of twice the acceleration of the first car. Assuming that it could maintain the same acceleration at higher speeds, how much time will this second car take to go from 0 to 120 mph?

14 s

A ball thrown at an initial angle of 37.0∘ and initial velocity vi = 24.0 m/s reaches a maximum height ℎ, as shown in (Figure 1). With what initial speed must a ball be thrown straight up to reach the same maximum height hℎ?

14.4 m/s

A car can go from 0 to 60 mph in 8.0 s . Assuming that it could maintain the same acceleration at higher speeds, how long would it take the car to go from 0 to 120 mph?

16 s

Riders on a Ferris wheel move in a circle with a speed of 4.50 m/s. As they go around, they experience a centripetal acceleration of 2.40 m/s2 . What is the diameter of this particular Ferris wheel?

16.9 m

Small-plane pilots regularly compete in "message drop" competitions, dropping heavy weights (for which air resistance can be ignored) from their low-flying planes and scoring points for having the weights land close to a target. A plane 65 m above the ground is flying directly toward a target at 46 m/s . At what distance from the target should the pilot drop the weight? The pilot looks down at the weight after she drops it. Where is the plane located at the instant the weight hits the ground?

170 m directly over the target

A car is skidding to a stop on a level stretch of road. Identify the number of the action/reaction pairs of forces between the car and the road surface.

2 pairs

The bacterium Escherichia coli (or E. coli) is a single-celled organism that lives in the gut of healthy humans and animals. Its body shape can be modeled as a 2-μm-long cylinder with a 1 μm diameter, and it has a mass of 1×10−12g. Its chromosome consists of a single double-stranded chain of DNA 700 times longer than its body length. The bacterium moves at a constant speed of 20 μm/s though not always in the same direction. Answer the following questions about E. coli using SI units (unless specifically requested otherwise) and correct significant figures. What is its length? What is its diameter? What is its mass? What is the length of its DNA, in millimeters? If the organism were to move along a straight path, how many meters would it travel in one day?

2 x 10^-6 m 1 x 10^-6 m 1 x 10^-15 kg 1 mm 2m

A student walks 1.6 mi west and then 1.6 mi north. Afterward, how far is she from her starting point?

2.3 mi

Scallops eject water from their shells to provide a thrust force. (Figure 1) shows a smoothed graph of actual data for the initial motion of a 25 g scallop speeding up to escape a predator. What is the magnitude of the net force needed to achieve this motion? How does this force compare to the 0.25 N weight of the scallop?

2.5 x 10^-2 N This force is 1/10 of the weight of the scallop.

A bird flies 3.6 km due west and then 2.1 km due north. Another bird flies 2.1 km due west and 3.6 km due north. What is the angle between the net displacement vectors for the two birds?

29 degrees

A football is kicked at an angle of 40 ∘ with a speed of 24 m/s . To the nearest second, how long will the ball stay in the air?

3 s

A rider on a water slide goes through three different kinds of motion, as illustrated in the figure below. Use the data and details from the figure to answer the following questions. What is the vertical component of the velocity of a rider as he or she hits the water? Suppose the designers of the water slide want to adjust the height ℎ above the water so that riders land twice as far away from the bottom of the slide. What would be the necessary height above the water? During which section of the motion is the magnitude of the acceleration experienced by a rider the greatest?

3.4 m/s 2.4 m The second

Heather and Jerry are standing on a bridge 51 m above a river. Heather throws a rock straight down with a speed of 17 m/s . Jerry, at exactly the same instant of time, throws a rock straight up with the same speed. Ignore air resistance. How much time elapses between the first splash and the second splash? Which rock has the faster speed as it hits the water?

3.5 sec both hit with equal speeds

Free Fall on Different Worlds Objects in free fall on the earth have acceleration ay=−9.8m/s2. On the moon, free fall acceleration is approximately 1/61/6 of the acceleration on earth. This changes the scale of problems involving free fall. For instance, suppose you jump straight upward, leaving the ground with velocity vi and then steadily slowing until reaching zero velocity at your highest point. Because your initial velocity is determined mostly by the strength of your leg muscles, we can assume your initial velocity would be the same on the moon. But considering the equation h=v22g we can see that, with a smaller free-fall acceleration, your maximum height would be greater. The following questions ask you to think about how certain athletic feats might be performed in this reduced-gravity environment. If an astronaut can jump straight up to a height of 0.6 m on earth, how high could he jump on the moon?

3.6 m

Compute 3.24 mm + 0.432 mm to the correct number of significant figures.

3.67

A car drives horizontally off a 75-m-high cliff at a speed of 29 m/s . Ignore air resistance. How long will it take the car to hit the ground? How far from the base of the cliff will the car hit?

3.9 s 110 m

Blades of grass grow from the bottom, so, as growth occurs, the top of the blade moves upward. During the summer, when your lawn is growing quickly, estimate this speed, in m/s. Make this estimate from your experience noting, for instance, how often you mow the lawn and what length you trim.

4 x 10^-8 m/s

A cannon, elevated at 40∘ is fired at a wall 300 m away on level ground, as shown in the figure below. The initial speed of the cannonball is 89 m/s.(Figure 1) How long does it take for the ball to hit the wall? At what height ℎ does the ball hit the wall?

4.4 s 160 m

A bird flies 3.8 km due west and then 2.4 km due north. What is the magnitude of the bird's displacement?

4.5 km

Motor neurons in mammals transmit signals from the brain to skeletal muscles at approximately 25 m/s Estimate how much time in ms (10−3s) it will take for a signal to get from your brain to your hand.

40 ms

If you kick a football, at what angle to the ground should you kick the ball for the maximum range - that is, the greatest distance down the field? At what angle to the ground should you kick the ball for the maximum "hang time" - that is, the maximum time in the air?

45 90

An object's average density ρ is defined as the ratio of its mass to its volume: ρ=M/V. The earth's mass is 5.94×10^24kg, and its volume is 1.08×10^12km3. What is the earth's average density?

5.50×10^3kg/m3

A 200 kg weather rocket is loaded with 100 kg of fuel and fired straight up. It accelerates upward at 30.0 m/s2 for 30.0 s, then runs out of fuel. Ignore any air resistance effects. What is the rocket's maximum altitude? How long is the rocket in the air? Choose the correct velocity-versus-time graph for the rocket from liftoff until it hits the ground.

54.8 km 228 s

A football is kicked at an angle of 35 ∘ with a speed of 24 m/s . How far will the ball travel?

55 m

Suppose a plane accelerates from rest for 30 s, achieving a takeoff speed of 80 m/s after traveling a distance of 1200 m down the runway. A smaller plane with the same acceleration has a takeoff speed of 56 m/s . Starting from rest, after what distance will this smaller plane reach its takeoff speed?

588 m

Formula One race cars are capable of remarkable accelerations when speeding up, slowing down, and turning corners. At one track, cars round a corner that is a segment of a circle of radius 95 m at a speed of 68 m/s. What is the approximate magnitude of the centripetal acceleration, in units of g?

5g

In 1780, in what is now referred to as "Brady's Leap," Captain Sam Brady of the U.S. Continental Army escaped certain death from his enemies by running over the edge of the cliff above Ohio's Cuyahoga River in (Figure 1), which is confined at that spot to a gorge. He landed safely on the far side of the river. It was reported that he leapt 22 ftft (≈≈ 6.7 mm) across while falling 20 ftft (≈≈ 6.1 mm). What is the minimum speed with which he'd need to run off the edge of the cliff to make it safely to the far side of the river? The world-record time for the 100 mm dash is approximately 10 ss. Given this, is it reasonable to expect Brady to be able to run fast enough to achieve Brady's leap?

6 m/s Yes, the obtained speed is less than the world-record.

On the earth, an astronaut can safely jump to the ground from a height of 1.3 m ; her velocity when reaching the ground is slow enough to not cause injury. From what height could the astronaut safely jump to the ground on the moon? On the earth, an astronaut throws a ball straight upward; it stays in the air for a total time of 3.1 s before reaching the ground again. If a ball were to be thrown upward with the same initial speed on the moon, how much time would pass before it hit the ground?

7.8 m 19 s

A garden has a circular path of radius 50 mm . John starts at the easternmost point on this path, then walks counterclockwise around the path until he is at its southernmost point. What is the magnitude of John's displacement? What is the direction of John's displacement?

71 m southwest

A car is traveling at vx = 24 m/s . The driver applies the brakes and the car decelerates at ax = -4.0m/s2 . What is the stopping distance?

72 m

The images of trees in the figure come from a catalog advertising fast-growing trees. If we mark the position of the top of the tree in the successive years, as shown in the graph in the figure, we obtain a motion diagram much like ones we have seen for other kinds of motion. The motion isn't steady, of course. In some months the tree grows rapidly; in other months, quite slowly. We can see, though, that the average speed of growth is fairly constant for the first few years. What is the tree's speed of growth, in feet per year, from t=1yr to t=3yr? What is the tree's speed in m/s? At the end of year 3, a rope is tied to the very top of the tree to steady it. This rope is staked into the ground 15 feet away from the tree. What angle does the rope make with the ground?

9 ft/yr 9 x 10^-8 m/s 63 degrees

A rider on a water slide goes through three different kinds of motion, as illustrated in the figure. Use the data and details from the figure to answer the following questions.(Figure 1) At the end of the first section of the motion, riders are moving at what approximate speed? Suppose the acceleration during the second section of the motion is too large to be comfortable for riders. What change could be made to decrease the acceleration during this section? What is the vertical component of the velocity of a rider as he or she hits the water? Suppose the designers of the water slide want to adjust the height above the water so that riders land twice as far away from the bottom of the slide. What would be the necessary height above the water? During which section of the motion is the magnitude of the acceleration experienced by a rider the greatest?

9 m/s Increase the radius of the circular segment. 3.4 m/s 2.4 m the second

Choose an example of a vertical motion with a negative velocity and a negative acceleration.

A ball dropped from a height during its downward motion.

Choose an example of a vertical motion with a positive velocity and a negative acceleration.

A ball thrown upward, before it starts to fall back down.

The bacterium Escherichia coli (or E. coli), is a single-celled organism that lives in the gut of healthy humans and animals. When grown in a uniform medium rich in salts and amino acids, it swims along zig-zag paths at a constant speed. (Figure 1) shows the positions of an E. coli as it moves from point A to point J. Each segment of the motion can be identified by two letters, such as segment BC. During which segments, if any, does the bacterium have the same displacement? During which segments, if any, does the bacterium have the same speed? During which segments, if any, does the bacterium have the same velocity?

AB and CD All paths AB and CD

Suppose you are an astronaut in deep space, far from any source of gravity. You have two objects that look identical, but one has a large mass and the other a small mass. How can you tell the difference between the two?

Assuming you can exert a reproducible force in throwing both objects, you could throw each and note the acceleration each obtains.

A car travels at constant speed along the curved path shown in (Figure 1). Five possible vectors are also shown in the figure; the letter E represents the zero vector. Which vector best represents the car's velocity at position 1? Which vector best represents the car's acceleration at point 1? Which vector best represents the car's velocity at position 2? Which vector best represents the car's acceleration at point 2? Which vector best represents the car's velocity at position 3? Which vector best represents the car's acceleration at point 3?

B - velocity 1 E - acceleration 1 C velocity 2 D - acceleration 2 B - velocity 3 A - acceleration 3

BETTY

BETTY

The figure below shows block A sitting on top of block B. A constant force F⃗ F→ is exerted on block B, causing block B to accelerate to the right. Block A rides on block B without slipping. Which statement is true?

Block B exerts a friction force on block A, directed to the right.

Tennis balls experience a large drag force. A tennis ball is hit so that it goes up and then comes back straight down. Direction of drag force is

Down and then up.

A person gives a box a shove so that it slides up a ramp, then reverses its motion and slides down. The direction of the force of friction is

Down the ramp and then up the ramp. Submit

A jet plane is speeding down the runway during takeoff. Air resistance is not negligible. Identify the forces on the jet

Drag, normal force, weight, thrust

Assume that you are pulling on the rope but the car is not moving. What is the approximate direction of the force of the mud on the car? Suppose your efforts work, and the car begins to move forward out of the mud. As it does so, the force of the car on the rope is

East Equal to the force of the rope on the car.

Three arrows are shot horizontally. They have left the bow and are traveling parallel to the ground as shown in the figure. Air resistance is negligible. Rank in order, from largest to smallest, the magnitudes of the horizontal forces F1, F2, and F3 acting on the arrows. Some may be equal. State your reasoning.

F1=F2=F3=0 because there is no change in the horizontal motion of the arrows.

The following options describe the motion of four cars. Which car has the largest acceleration?

Goes from 0 m/s to 3.8 m/s in 1.0 s

A Porsche challenges a Honda to a 400 m race. Because the Porsche's acceleration of 3.4 m/s2 is larger than the Honda's 3.0 m/s2, the Honda gets a 110 m head start - it is only 290 m from the finish line. Assume, somewhat unrealistically, that both cars can maintain these accelerations the entire distance. Who wins the race? By how much time does the winner win?

Honda 1.4 sec

In physics, every physical quantity is measured with respect to a unit. Time is measured in seconds, length is measured in meters, and mass is measured in kilograms. Knowing the units of physical quantities will help you solve problems in physics. Gravity causes objects to be attracted to one another. This attraction keeps our feet firmly planted on the ground and causes the moon to orbit the earth. The force of gravitational attraction is represented by the equation F=Gm1m2r2, where F is the magnitude of the gravitational attraction on either body, m1 and m2 are the masses of the bodies, r is the distance between them, and G is the gravitational constant. In SI units, the units of force are kg⋅m/s2kg⋅m/s2, the units of mass are kgkg, and the units of distance are mm. For this equation to have consistent units, the units of G must be which of the following?

m^3/kg*s^2

The figure shows the position graph of a car traveling on a straight road. (Figure 1) The velocity at instant 1 is _________ and the velocity at instant 2 is _________.

negative, negative

Alyssa pushes to the right on a filing cabinet; the friction force from the floor pushes on it to the left. Because the cabinet doesn't move, these forces have the same magnitude. Do they form an action/reaction pair?

no

Suppose two vectors have unequal magnitudes. Can their sum be 0?

no

Shannon decides to check the accuracy of her speedometer. She adjusts her speed to read exactly 70 mph on her speedometer and holds this steady, measuring the time between successive mile markers separated by exactly 1.00 mile. If she measures a time of 47 s , is her speedometer accurate? If not, is the speed it shows too high or too low?

no too low

You throw a rock upward. The rock is moving upward, but it is slowing down. If we define the ground as the origin, the position of the rock is _____ and the velocity of the rock is _____.

positive, positive

The minimum stopping distance for a car traveling at a speed of 30 m/s is 60 m, including the distance traveled during the driver's reaction time of 0.50 s . Select the correct position-versus-time graph for the motion of the car. Assume the car is at xi= 0 m when the driver first sees the emergency situation ahead that calls for a rapid halt. What is the minimum stopping distance for the same car traveling at a speed of 43 m/s ?

quadratic graph 110 m

A sports car is advertised as capable of "reaching 60 mph in 5 seconds flat, cornering at 0.85g, and stopping from 70 mph in only 168 feet." In which of those three situations is the magnitude of the car's acceleration the largest? In which of those three situations is the magnitude of the car's acceleration the smallest?

stopping from 70 mph in 168 ft reaching 60 mph in 5 seconds

A Thompson's gazelle can reach a speed of 13 m/s in 3.0 s . A lion can reach a speed of 9.5 m/s in 1.0 s. A trout can reach a speed of 2.8 m/s in 0.12 s. Which animal has the greatest acceleration?

trout

For a projectile, which of the following quantities are constant during the flight: x, y, vx, vy, v, ax, ay? Which of the quantities are zero throughout the flight?

vx, ax, ay ax

A tennis player hits a ball 2.0 m above the ground. The ball leaves his racquet with a speed of 20 m/s at an angle 5.0 ∘ above the horizontal. The horizontal distance to the net is 7.0 m, and the net is 1.0 m high. Does the ball clear the net? if so, by how much? If not, by how much does it miss?

yes 1 m

shows the motion diagram for a rider on a Ferris wheel that was turning at a constant speed. The inset to the figure shows how to find the acceleration vector at the rightmost point. Use a similar analysis to find the rider's acceleration vector at the LEFTMOST position of the motion diagram in (Figure 2). Find the rider's acceleration vector at the HIGHEST position of the motion diagram in (Figure 3). Find the rider's acceleration vector at the LOWEST position of the motion diagram in (Figure 3).

Δv = v7 - v6 Δv = v4 - v3 Δv = v9 - v8