Q: Three identical very dense masses of $$4000\ \mathrm{kg}$$ each are placed on the x-axis. One mass is at $$x = -1.30\ \mathrm{m}$$, one at the origin, and one at $$x = +1.30\ \mathrm{m}. $$What is the magnitude of the net gravitational force on the mass at the origin due to the other two masses?

$$9.5 \times 10$$^{-7}$$\ \mathrm{N}$$

Question 1

A ball is launched at 25 m/s on level ground at an angle so that it undergoes projectile motion. During the flight of the ball, the maximum speed is 31 m/s. What is the approximate speed of the ball when it reaches the maximum height in the flight? Neglect air resistance.

Accepted Answer

$$25\ \mathrm{m/s}$$

Question 2

A 2.5 kg block is stationary on a ramp that is inclined at $$26^\circ$$ from horizontal as shown. The coefficient of static friction between the box and the ramp surface is $$0.15. $$What is the magnitude of the static friction force of the ramp on the box?

Accepted Answer

$$6\ \mathrm{N}$$

Question 3

Suppose a car is going around a banked circular curve while remaining at the same altitude. The figure at right shows the top and front view of the car. The velocity of the car at the instant shown in the top view is directed toward the bottom of the page, and its magnitude is increasing. Which of the choices below best represents the directions of the acceleration of the car in the top and front views?

Accepted Answer

Top view: toward center and forward; Front view: up the incline and forward

Question 4

A 2.5 kg box is initially hanging at rest from a rope. Now the rope is pulled upward. When the box is 3.2 m above where it was before, the box is moving with speed of $$1.5\ \mathrm{m/s}. $$How much work was done on the box by the force started it upward?

Accepted Answer

$$85\ \mathrm{J}$$

Question 5

A 53 kg skydiver is falling through the air. At $$v_t$$, she reaches her terminal speed. Between $$t = 0$$ and $$t = 1.0\ \mathrm{s}$$, $$500\ \mathrm{J} of $$thermal energy is created through air resistance. What is the fall distance between $$t = 0$$ and $$t = 1.0\ \mathrm{s}$$?

Accepted Answer

$$9.4\ \mathrm{m}$$

Question 6

The figure shows a potential energy diagram for an object-earth system. The object has a mass of $$0.20\ \mathrm{kg}$$ and oscillates between $$2.0\ \mathrm{m}$$ and $$8.0\ \mathrm{m} as $$shown. What is the maximum speed of the object?

Accepted Answer

$$3.2\ \mathrm{m/s}$$

Question 7

Two uniform iron beams are joined end-to-end as shown to make a single object. The left beam is $$1.2\ \mathrm{kg}$$ and $$1.00\ \mathrm{m}$$ long, and the right beam is $$0.8\ \mathrm{kg}$$ and $$2.00\ \mathrm{m}$$ long. How far from the left end of the left beam is the center of mass of the object?

Accepted Answer

$$1.4\ \mathrm{m}$$

Question 8

Suppose that a uniform thin rod of length $$0.82\ \mathrm{m} is $$pivoted at the floor and can swing vertically as a simple pendulum. At a certain instant, the rod is rotating about the pivot at an angular speed of $$4.0\ \mathrm{rad/s}$$, and is at an angle $$	heta$$ from the vertical. What is the tangential acceleration of the end of the rod at this instant?

Accepted Answer

$$a_t = r\$$omega^2$$

Question 9

Three $$0.50\ \mathrm{kg}$$ masses are connected by massless, rigid rods as shown. What is the magnitude of the net force on the assembly through the center of mass?

Accepted Answer

$$0\ \mathrm{N}$$

Question 10

If the mass of the uniform rod is $$15\ \mathrm{kg}$$, what is the tension in the rope?

Accepted Answer

$$150\ \mathrm{N}$$

Question 11

What is the magnitude of the angular momentum relative to the origin of the $$0.53\ \mathrm{kg}$$ particle shown?

Accepted Answer

$$3.5\ \mathrm{kg\cdot m^2$/s}$$

Question 12

Three identical very dense masses of $$4000\ \mathrm{kg}$$ each are placed on the x-axis. One mass is at $$x = -1.30\ \mathrm{m}$$, one at the origin, and one at $$x = +1.30\ \mathrm{m}. $$What is the magnitude of the net gravitational force on the mass at the origin due to the other two masses?

Accepted Answer

$$9.5 	imes 10$$^{-7}$$\ \mathrm{N}$$

Question 13

A rocket is launched straight up from the Earth's surface at a speed of $$9000\ \mathrm{m/s}. $$What is its speed when it is very far away from the earth? (Radius of Earth = $$6.4 	imes 10^6$\ \mathrm{m}$$, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$8.7\ \mathrm{km/s}$$

Question 14

A GPS satellite orbits Earth at an altitude (distance above the surface of the Earth) of $$2.02 	imes 10^7$\ \mathrm{m}. $$How long does it take for the satellite to complete one complete orbital revolution? (Radius of Earth = $$6.4 	imes 10^6$\ \mathrm{m}$$, mass of Earth = $$6.0 	imes 10$$^{24}$$\ \mathrm{kg})$$

Accepted Answer

$$12\ \mathrm{hours}$$

Question 15

A group of students has conducted Lab 02 to determine the coefficient of static friction between a shoe and a wooden board. In their experiment, they placed an empty shoe on the board and changed the angle of the board. The shoe started to move when the board was at an angle of $$34^\circ$$ with the horizontal. They now place an object of mass $$0.5\ \mathrm{kg} in $$the shoe and repeat the experiment. Which of the following best represents the angle at which the shoe should start to move?

Accepted Answer

At approximately $$34^\circ$$

Question 16

A student uses a digital scale to measure the mass of an object. They find the reading on the scale is $$14.6\ \mathrm{g}. $$How should they report the mass according to the rules developed in the lab?

Accepted Answer

$$14.6 \pm 0.1\ \mathrm{g}$$

Question 17

Two identical pucks are held the same height above the floor. A thread connects and runs through a small, light, frictionless pulley as shown. At the same instant, both pucks are released from rest. What is the speed of A at the floor, after B at the same instant is speed $$v$$?

Accepted Answer

$$v$$

Question 18

A car moves clockwise at constant speed around the oval track shown. Let $$|\Delta v_{AB}| be $$the magnitude of the change in velocity from point A to point B and $$|\Delta v_{CD}| be $$the magnitude of the change in velocity from point C to point D. Which of the following best represents the relationship between the magnitudes of the velocity changes?

Accepted Answer

$$|\Delta v_{AB}| = |\Delta v_{CD}|$$

Question 19

Two experiments are performed with the same puck and rod on a level, frictionless table. In each experiment, the puck moves with initial velocity only, as shown. In Experiment 1, the rod is initially at rest, and the puck sticks to the rod after the collision. The puck and the rod have the same mass. In Experiment 2, the puck moves toward the center of the rod. Is the final speed of the center of mass the system in experiment 1 greater than, less than, or equal to that in experiment 2?

Accepted Answer

Equal to

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