Test 5 APCB

B.22 An object starts at rest and moves in a horizontal circle such that its tangential speed increases linearly as a function of time. Which of the following graphs shows how the centripetal acceleration behaves as a function of time?

(exponentially up) | ~ | ~ | ~~~ |_~~~~~__________

B.11 A car travels with a tangential speed v1 around a curve of radius r and turns to the left, as shown by the rear view of the car in Figure 1. A force diagram of the forces exerted on the car with speed of 5m/s as it turns is shown in Figure 2. A force diagram of the forces exerted on the car with speed v as it turns around the same curve of the same radius with the same tangential speed is shown in Figure 3. The speed v of the car is most nearly

15m/s

A.4 A moon orbits a planet in a nearly circular orbit of radius R, as shown in the figure. The moon has a mass of 1×1022 kg, and the gravitational field strength at a distance R from the planet is 0.001 N/kg. What is the gravitational force exerted on the moon while it is in orbit around the planet?

1x10^19 N

A.19 A moon of mass 1×1020 kg is in a circular orbit around a planet. The planet exerts a gravitational force of 2×1021 N on the moon. The centripetal acceleration of the moon is most nearly

20 M/S^2

A.6 Two containers of water can have their individual masses varied by adding or removing water. The containers are initially a distance d apart, as measured from their centers, and are filled with water so that each has a mass M, as shown in Figure 1 above. The gravitational force that one container exerts on the other is F0. Water is then added to one container so that its mass increases to 1.5M, and water is removed from the other container so that its mass decreases to 0.5M, as shown in Figure 2. What is the new gravitational force exerted on one container by the other?

3/4 F0

B.8 At one point in their individual orbits, three planets, X,Y,& Z, are along the same horizontal line. The gravitational force on Planet X from Planet Z is F0. The distance from the center of mass of each planet to an adjacent planet is given in terms of R0, and their respective masses are given in terms of M0, as shown above. What is the net force on Planet Y, and what reasoning supports this claim?

5F0 to the right, because the gravitational force from Planet Y is greater than the gravitational force from Planet X.

A.17 A 2 kg object is released from rest near the surface of a planet with a negligible atmosphere. A graph of the object's speed v as a function of time t is shown. What is the weight of the object on the planet? A

8N

A.18 An object of mass M is placed on a disk that can rotate. One end of a string is tied to the object while the other end of the string is held by a pole that is located at the center of the disk. Initially, the object is spun in a horizontal circle of radius R at a constant tangential speed of v0, as shown in the figure, such that the tension in the string is T. At a later time, the disk is spun such that the tangential speed of the object is increased to 2v0 . At a later time, the tangential speed of the object is increased to 3v0 . Which of the following diagrams could represent the forces exerted on the object at one of the given speeds? Assume that the force of static friction is negligible. Select two answers.

9T--------------- 4t----------

B.2 Consider a runner in any of the lanes moving at a known, constant tangential speed. Which of the following measuring tools, if any, could be used to experimentally determine the centripetal acceleration of the runner?

A meterstick

A.13 A scientist designs an experiment that requires two atomic particles whose only fundamental force exerted between them is the gravitational force. Which combination of particles and separation distance will meet this condition?

A proton and neutron located 1.0 mm apart

A.20 In which of the following situations is the gravitational force the dominant force? Select two answers.

A satellite is in orbit around a planet. An object is in free fall just after it is released from rest.

A.15 A student must determine the inertial mass of a block attached to a horizontal track. The block is free to move horizontally along the track, as shown above. Frictional forces are considered to be negligible. The student may only choose two measuring tools to determine the inertial mass of the block. What tools should the student choose? Select two answers.

Accelerometer Force sensor

B.7 A student conducts three experiments to determine how certain quantities influence the centripetal force responsible for an object to spin in a horizontal circle. The student uses one end of a string to attach the object while the other end is connected to a force sensor that allows the student to change the tension on the string, as shown in the figure. The student records data from the three experiments in the table above. Which of the following experiments, if any, collected data that do not agree with the expression for the net centripetal force on the object? (Big Chart)

All the data are expected.

B.9 A planet orbits a star in the path shown in the figure (ellipse). The planet's mass is much smaller than the star's mass. Which two of the following claims are correct about the accelerations associated with the planet, star, and planet-star system? Select two answers. Justify your selections.

Both the planet and the star accelerate, because each object exerts a force on the other object. The center of mass of the planet-star system does not accelerate, because there is no net force exerted on the system.

B.3 Now consider four runners running around the track with the same constant tangential speed, with one runner in each lane of the track. A student is considering using the following equations to determine which runner has the greatest acceleration. Equation 1: v^2x=v^2x0+2ax(x−x0) Equation 2: ac=v^2/r Which equation should the student use, and why?

Equation 2, because the radius of the circular path traveled by a runner determines the acceleration of the runner.

A.9 Two experiments are conducted are conducted to determine the mass of an object. In Experiment 1, the object's weight is measured by using an electronic balance once the object has been placed at rest on the balance. In Experiment 2, the object is pulled along a horizontal surface with a spring scale such that the force reading on the spring scale remains constant while a motion detector is used to measure the instantaneous speed of the object as it is pulled. All frictional forces for both experiments are considered to be negligible. Which of the two experiments, if either, could be used to determine the gravitational mass of the object?

Experiment 1 only

B.5 A student swings a ball of mass M on the end of a string in a vertical circle of radius R, as shown in the top figure above. Also shown is a diagram representing all of the forces exerted on the ball at the bottom of the circle, where its speed is v0. What is the magnitude of the acceleration of the ball at the bottom of the circle?

F(tension) - F (gravity) ------------------------- M

B.1 Consider a runner in lane 1 with a speed v1 and a runner in lane 4 with a speed v4, where the ratio of the speeds v4/v1 is 2. The radius of lane 4 is b times the radius of lane 1, and both runners have the same mass. Which of the following claims is correct about the net forces F1 and F4 exerted on the runners in lanes 1 and 4, respectively?

F4 is equal to 4/b F1.

A.1 Planet X has a mass of M and a radius of R. Planet Y has a mass of 3M and a radius of 3R. Identical satellites orbit both planets at a distance R above their surfaces, as shown above. The planets are separated by such a large distance that the gravitational forces between them are negligible. How does the magnitude of the gravitational force FY exerted by Planet Y on its satellite compare to the gravitational force FX exerted by Planet X on its satellite?

FY=3/4FX

B.21 Two satellites orbit a planet of mass M, as shown above. Satellite A of mass 2m travels in a circular orbit of radius R. Satellite B of mass m travels in a circular orbit of radius 2 R. Each satellite travels at a constant tangential speed. How does the gravitational force, FgA, exerted on satellite A from the planet compare with the gravitational force, FgB, exerted on satellite B from the planet?

FgA is larger than FgB because satellite A is twice as large as satellite B and is half the distance to the planet as satellite B.

B.18 A satellite orbits Earth in a circular path at a constant tangential speed, as shown in the figure. Which of the following correctly represents the directions of the net force FNet , acceleration a, and tangential velocity vT of the satellite at the instant shown in the figure?

Fnet a vT _________________________ ^ ^ ---> | |

B.14 One end of a string is attached to a ball, with the other end held by a student such that the ball is swung in a horizontal circular path of radius R at a constant tangential speed. At a later time, the tension force exerted on the ball remains constant, but the length of the string is decreased to R/4. What is the new tangential speed of the ball?

Half the original speed

B.16 (girl swinging a rope) A student must test the maximum force exerted on an object attached to a string before the string breaks. The student ties the object of mass m0 to one end of the string and then uses the other end of the string to spin the object at a constant speed so that the object travels in a horizontal circular path, as seen in Figure 1. Figure 2 shows the horizontal force exerted on the object at time t0. In a second trial, what should the student do to increase the tension in the string while keeping all other quantities constant? Select two answers.

Increase the mass of m0. Decrease the time required for one rotation.

B.6 The figure above shows two identical asteroids that are located near each other but are not in contact. Various locations are also labeled on the asteroids. If an astronaut wants to stand on one of the asteroids and experience the largest net gravitational force, where should the astronaut stand?

Location A (far left or the "outside")

A.12 An Atwood machine is placed on a planet in which the acceleration due to gravity on the planet is unknown. Both ends of a light string are attached to two blocks such that M1>M2 , and the string passes through a pulley such that frictional forces are considered to be negligible, as shown above. The same tension force T is exerted on both blocks, and the block of mass M1 experiences an acceleration a0 in the downward direction when released from rest. Which quantities would allow the acceleration due to gravity on the planet to be determined?

M1 , M2 , and a0

A.16 A rocket on Earth experiences an upward applied force from its thrusters. As a result of this force, the rocket accelerates upward at 2 m/s2. Assume that there are no other upward forces exerted on the rocket and that wind resistance is negligible. Which of the following combinations of the rocket's mass mRocket and force from its thrusters FThrusters would result in an upward acceleration of 2 m/s2? Select two answers.

MRocket 1kg FThrusters 12N MRocket 3kg FThrusters 36N

B.17 A block is at rest on a disk that spins about its center, as shown. A student must determine the centripetal acceleration of the block when the block spins with the disk as a result of the force of static friction. What measuring devices, when used together, could be used to determine the centripetal acceleration of the block? Select two answers.

Meterstick Stopwatch

A.8 A student must conduct two experiments so that the inertial mass and gravitational mass of the same object can be determined. In the experiment to find the object's gravitational mass, the student ties one end of a string around the object with the other end tied to a spring scale so that the object can vertically hang at rest. In the experiment to find the object's inertial mass, the student uses a spring scale to pull the object, starting from rest, across a horizontal surface with a constant applied force such that frictional forces are considered to be negligible. In addition to the spring scale, the student has access to other measuring devices commonly found in a science laboratory. Which of the following lists the essential measuring devices the student can use to collect the data necessary to find the object's gravitational and inertial mass?

Meterstick and timer

A.22 Student X ties one end of a string to a 0.5 kg ball and swings the ball in a vertical circle of radius 1 m, as shown in the figure. Student Y uses video analysis to determine the speed of the ball at points A, B, C, and D, as shown in the table. Student X states that the data are incorrect because the tension in the string provides a centripetal force that should cause the ball to travel with a constant tangential speed. Is Student X's reasoning correct, and why or why not?

No, because the net centripetal force exerted on the ball is the combination of the tension force from the string and the force due to gravity from Earth.

A.21 A student uses a motion sensor to collect data about an object's velocity v as a function of time t after it is released from rest near Earth's surface. The student claims that the graph shown represents the object while in free fall. Does the data from the graph support the student's claim?

No, because the slope of the curve of the graph indicates that the acceleration is less than gg, which indicates that a force other than gravity is exerted on the object.

A.3 A moon orbits a planet in a nearly circular orbit of radius R, as shown in the figure. Which of the following free-body diagrams could be used to analyze the forces exerted on the moon when it is at the position indicated in the figure?

O---------> F gravity

A.11 An object is placed on a rotating disk. The amount of time it takes the object to make one revolution around the center of the circle may be set at a known value. Which of the following procedures could be used to make the necessary measurements to find the coefficient of static friction between the object and the disk's surface?

Place the object on the disk and measure the distance from the center of the disk to the center of mass of the object by using a meterstick. Slowly increase the rate the disk rotates until the object begins to slide off the disk. Record the time in which the object makes one revolution around the center of the disk.

B.13 Planet X is in a stable circular orbit around a star, as shown above. Which of the following graphs best shows the tangential speed of the planet as a function of its horizontal position from point A to point B if the planet is moving counter clockwise as viewed in the figure above?

Speed | |~~~~~~~~~~~~ | |________________ position

A.14 A ball of Mass M is swung in a vertical circle with a constant tangential speed. Figure 1 shows the forces exerted on the ball at the top of the circle, and Figure 2 shows the forces exerted on the ball at the bottom of the circle. Which of the following is an expression for the centripetal acceleration of the ball in terms of M, T1, T2, and any fundamental constants?

T1+T2/2M

B.19 A square block is attached to a string of negligible mass and moves in a horizontal circle at a constant speed. The string passes through a vertical tube, and its other end is attached to a cylinder, as shown in the figure. Which of the following claims can be made by relating one of Newton's laws of motion to an object that travels in uniform circular motion?

The block exerts a force on the string.

B.15 A long wooden board is at rest on a horizontal surface, and there is negligible friction between the board and the surface. A block is sliding along the board, and there is friction between the block and the board. At the instant shown in the figure, the block is moving but the board is still at rest. What happens to the board and block after the instant shown, and what reasoning supports this claim?

The board starts moving in the same direction as the block and the block is slowing down, because the board exerts a force on the block and the block exerts a force on the board.

A.5 A moon orbits a planet in a nearly circular orbit of radius R, as shown in the figure. Astronomers making careful observations of the moon's orbit discover that the orbit is not perfectly circular, nor is it elliptical. Which of the following statements supports this observation?

There is another celestial body that exerts a gravitational force on the moon.

B.20 (straight graph down and to the left) An object falls toward Earth after it is released from rest, as a result of Earth's gravitational force. A student uses a motion detector to create the graph of the object's displacement as a function of the squared time in which the object was in free fall. How can the student use the graph to determine the acceleration ay of the object while in free fall?

Use the slope of the graph and set it equal to 1/2ay to then solve for ay

A.10 A student analyzes data of the motion of a planet as it orbits a star that is in deep space. The orbit of the planet is considered to be stable and does not change over time. The student claims, "The only experimentally measurable external force exerted on the planet is the force due to gravity from the star." Is the student's claim supported by the evidence? What reasoning either supports or contradicts the student's claim?

Yes. Other external forces are exerted on the planet, but they are of negligible magnitude.

B.4 A truck in a traffic circle travels in a circular path at constant speed v0 while passing through region X of the circle, as shown in Figure 1 above. A diagram representing the forces exerted on the truck in region X is shown in Figure 2. At a later time a car with less mass than the truck passes through region X at the same speed and the same distance from the center of the traffic circle as the truck. The coefficient of friction between the car's tires and the ground is the same as that for the truck's tires and the ground. Which of the following diagrams could represent the forces exerted on the car in region X compared to the truck in region X ? Assume that the length of each arrow is proportional to the magnitude of the force represented by the arrow.

^ normal | | <-O friction | | ^ gravity

A.7 Satellite A orbits a planet at a distance d from the planet's center with a centripetal acceleration a0. A second identical satellite B orbits the same planet at a distance 2d from the planet's center with centripetal acceleration ab. What is the centripetal acceleration ab in terms of a0 ?

a0/4

A.2 Planet X has a mass of M and a radius of R. Planet Y has a mass of 3M and a radius of 3R. Identical satellites orbit both planets at a distance R above their surfaces, as shown above. The planets are separated by such a large distance that the gravitational forces between them are negligible. How does the gravitational field gX at the surface of Planet X compare with the gravitational field gY at the surface of Planet Y?

gx=3gy

B.10 A satellite moves in a circular orbit at a constant speed v0 around Earth at a distance R from its center. The force exerted on the satellite is F0. An identical satellite orbits Earth at a distance of 3R from the center of the Earth. How does the tangential speed, vT, of the satellite at distance 3R compare to the speed v0 of the satellite at R?

vT= (1 / √3) x v0

B.12 A student places a block on a disk, and the edge of the disk makes one revolution in a constant time interval △t. A force probe is attached to the block and the center of the disk, as shown above. In an experiment, a student measures the centripetal force exerted on the block when placed at various distances from the center of the disc while the tangential speed of the edge of the disc remains constant. Which of the following graphs shows the centripetal force exerted on the block as a function of its distance from the center of the disk?

| @ | @ |@_________