Question 1

A 2.1 m/s student, who is initially at rest, wants to catch a Frisbee. When the Frisbee passes over her head in a straight line at a speed of 4.1 m/s, she runs after it in the same direction as the Frisbee, maintaining a constant velocity. The Frisbee is accelerating at a rate of $$1.5 \ \mathrm{m/s^2$}. $$How long will it take the student to catch the Frisbee?

Accepted Answer

$$t = 3.3 \ \mathrm{s}$$

Question 2

Which of the following graphs best represents the position of the student and the Frisbee as a function of time if the student starts from rest at the location of the launch and only the Frisbee has an initial velocity?

Accepted Answer

Graph (a): Both lines start at the same point, Frisbee line has a steeper slope.

Question 3

Which of the following statements best describes the motion of an object that has a constant net force acting on it?

Accepted Answer

Its acceleration must be in the same direction as the force.

Question 4

A baseball player wants to hit a home run over the far wall of a stadium. He hits the ball 1 meter above the ground at an initial speed of $$30.0 \ \mathrm{m/s}$$ and such that it makes an angle of $$30^\circ$$ with respect to the horizontal. What is the tallest wall the player could clear 120 m away?

Accepted Answer

$$h = 3.12 \ \mathrm{m}$$

Question 5

Two blocks, one of mass $$M_1$$ and one of mass $$M_2$$, are in contact with each other on a frictionless floor. A horizontal force $$F = 72 \ \mathrm{N} is $$applied to block $$M_1$$, as shown. What is the force $$F_{12} of $$the block of mass $$M_2 on $$the block of mass $$M_1$$?

Accepted Answer

$$F_{12} = 54 \ \mathrm{N}$$

Question 6

Suppose now that $$F = 72 \ \mathrm{N}$$ and $$M_2 = 8$$ \ \mathrm{kg}$$ again, but a coefficient of kinetic friction $$\mu_k = 0.1$$ between the floor and each of the blocks is introduced. The magnitude of the static force acting on M_2$ is now:

Accepted Answer

smaller than it was without friction.

Question 7

Two stones are thrown simultaneously down a height of 500 m. The first stone is thrown vertically downward at a speed of $$10 \ \mathrm{m/s}$$, the second stone is thrown vertically upward at a speed of $$10 \ \mathrm{m/s}. $$Immediately after the two stones are thrown, the difference in their speeds ($$v_{down} - v_{up}) $$will:

Accepted Answer

stay the same.

Question 8

During the entire interval that both stones are in flight, the difference in their velocities will:

Accepted Answer

stay the same.

Question 9

How long will it take the second stone to get back down to the level from which it was thrown?

Accepted Answer

$$t = 14.3 \ \mathrm{s}$$

Question 10

A block of mass $$M = 2.5 \ \mathrm{kg} is on a $$stationary inclined plane that makes an angle $$	heta = 30^\circ$$ with the horizontal. A horizontal rope is attached to the block and pulls it up the incline. The block is held in place by the rope. The coefficient of static friction is $$\mu_s = 0.7$$ and the coefficient of kinetic friction is $$\mu_k = 0.5. $$Which of the following is the correct free-body diagram for the block?

Accepted Answer

Diagram with $$F_{Tension} up $$the incline, $$N$$ perpendicular to the surface, $$Mg$$ down, $$F_{friction} up $$the incline.

Question 11

A projectile is fired from a submarine traveling horizontally at $$20 \ \mathrm{m/s}$$ with respect to the water as shown in the figure. According to an observer on the submarine, the projectile is fired at $$45^\circ$$ with an initial velocity of $$60 \ \mathrm{m/s}. $$After firing the projectile, the submarine continues at $$20 \ \mathrm{m/s}. $$According to an observer watching from a buoy that is stationary with respect to the water, what will be the angle $$	heta$$ that the projectile makes with respect to the horizontal when it is launched?

Accepted Answer

$$	heta = 53^\circ$$

Question 12

A tough captain asks the submarine officer the projectile, but to him it looks like the projectile is moving straight up (relative to the submarine). What is the velocity of the projectile with respect to the water?

Accepted Answer

$$20 \ \mathrm{m/s} in $$the opposite direction the submarine is moving

Question 13

A block (kg) is hanging over the edge after a frictionless table and is attached to a block (kg) by a massless string. A massless, compressible spring (constant $$k = 130 \ \mathrm{N/m}) is $$attached to the block on the table. The spring is compressed a distance $$x$$ from its relaxed length $$X_0 if $$the system is in equilibrium. By how much is the spring compressed or unstretched relative to its relaxed length $$X_0 if $$the system is in equilibrium?

Accepted Answer

The spring is compressed by $$0.377 \ \mathrm{meters}.$$

Question 14

A student twirls a tennis ball of mass $$m at $$the end of a string of length $$r in a $$vertical circle. What is the minimum speed $$v_{min}$$ required to just keep the string taut at the top of its path?

Accepted Answer

$$v_{min} = \sqrt{g r}$$

Question 15

Suppose the string is cut when the ball is at the top of its travel and its velocity is $$v_y. $$After the string is cut, the only forces on the ball are:

Accepted Answer

the half's weight only.

Question 16

A satellite is put into a uniform circular orbit around the earth. The radius of the satellite's orbit is $$R_s = 4.2 	imes 10^7$ \ \mathrm{m} ($$measured from the center of the earth). The satellite has a mass of $$45 \ \mathrm{kg}. $$What is the speed of the satellite?

Accepted Answer

$$v = 3.2 \ \mathrm{km/s}$$

Question 17

If the mass of the satellite were doubled but the radius of its orbit was kept the same, its speed would:

Accepted Answer

stay the same.

Comprehensive Study Notes: Classical Mechanics and Rotational Dynamics

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