Physics Units 1-3

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

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

A student sets up an experiment to determine the inertial mass of a cart. The student has access to the following measurement equipment: a spring scale, a meterstick, and a stopwatch. The student uses the spring scale to pull the cart starting from rest along a horizontal surface such that the reading on the spring scale is always constant. All frictional forces are negligible. In addition to the spring-scale reading, which two of the following quantities could the student measure with the available equipment and then use to determine the inertial mass of the cart? Select two answers.

1) The total distance traveled by the cart after it has been in motion 2) The time during which the cart is in motion

A satellite orbits Earth. The only force on the satellite is the gravitational force exerted by Earth. How does the satellite's acceleration compare to the gravitational field at the location of the satellite? Select two answers.

1. The gravitational field and the acceleration point in the same direction. 2. The magnitudes of the acceleration and the gravitational field strength are equal.

A student must design an experiment to determine the acceleration of a cart that rolls down a small incline after it is released from rest. The student has access to a timer, a meterstick, and a slow-motion camera that takes a photograph every 160 of a second. The angle that the incline makes with the horizontal is unknown, and the length of the incline is unknown. Which of the following procedures could the student use to determine the cart's acceleration? Select two answer

1. Use the timer to record the time it takes the cart to travel alongside a meterstick that is attached to the incline. 2. Use the slow-motion camera to film the cart as it rolls down the incline alongside a meterstick that is attached to the incline.

The table shows the vertical position as a function of time for an object that is dropped from a height of 5 m. A student must determine the acceleration of the object. Which of the following procedures could the student use to make the determination? Justify your selections. Select two answers.

1. Use y=y0+vy0t+12ayt2y=y0+vy0t+12ayt2, since all quantities are known except for the acceleration due to gravity. 2. Create a position-versus-time graph of the ball's motion, and use the data to create a velocity-versus-time graph of the ball's motion, since the slope of the velocity-versus-time graph represents the acceleration.

Identical objects, Object X and Object Y, are tied together by a string and placed at rest on an incline, as shown in the figure. The distance between the center of mass of each object is 2m. The system of the two objects is released from rest, and a graph of the system's center of mass velocity as a function of time is shown. Based on the data, approximately how much time will it take the center of mass of Object X to reach point J near the bottom of the incline?

3.0 s

A 5kg object is released from rest near the surface of a planet such that its gravitational field is considered to be constant. The mass of the planet is unknown. After 2s, the object has fallen 30m. Air resistance is considered to be negligible. What is the gravitational force exerted on the 5kg object near the planet's surface?

75N

Car X and car Y travel on a horizontal surface along different parallel, straight paths. Each car's velocity as a function of time is shown in the graph. Which of the following claims is correct about car X and car Y?

Both car X and car Y travel in the same direction.

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

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=(3/4)FX

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 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

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.

Rock X is released from rest at the top of a cliff that is on Earth. A short time later, Rock Y is released from rest from the same location as Rock X. Both rocks fall for several seconds before landing on the ground directly below the cliff. Frictional forces are considered to be negligible. After Rock Y is released from rest several seconds after Rock X is released from rest, what happens to the separation distance S between the rocks as they fall but before they reach the ground, and why? Take the positive direction to be downward.

S increases because at all times Rock X falls with a greater speed than Rock Y .

Two objects, X and Y, move toward one another and eventually collide. Object X has a mass of 2M and is moving at a speed of 2v0 to the right before the collision. Object Y has a mass of M and is moving at a speed of v0 to the left before the collision. Which of the following describes the magnitude of the forces F the objects exert on each other when they collide?

The force exerted by X on Y is F to the right, and the force exerted by Y on X is F to the left.

A student pulls a block over a rough surface with a constant force FP that is at an angle θ above the horizontal, as shown above. If FP remains constant but the angle θ is increased, which of the following is true at some later time?

The force of friction between the block and surface will decrease.

A spring-loaded launcher has a mass of 0.60 kg and is placed on a platform 1.2m above the ground. The force of friction is negligible between the platform and the launcher. The launcher fires a 0.30kg ball that lands a distance D to the right of the platform, as shown in the diagram above. Which of the following explanations is true?

The launcher will fall off the platform and land D/2 to the left of the platform because the launcher is twice the mass of the ball.

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.

A student uses an electronic force sensor to study how much force the student's finger can apply to a specific location. The student uses one finger to apply a force on the sensor, and data collected from two trials are shown in the table. During which trial, if any, does the student's finger experience the greatest electromagnetic force?

Trial 2, because the student's finger applied the largest force to the sensor.

Which of the following experiments could be used to determine the inertial mass of a block?

Use a spring scale to exert a force on the block. Measure the acceleration of the block and the applied force.

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.

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

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