Q: A projectile is launched from the ground with an initial speed $$v_0 at an $$angle $$\theta$$ above the horizontal, as shown in the image. What is the maximum height $$H$$ reached by the projectile? (Neglect air resistance.)

$$H = \frac{v_0$^2 \sin^2$ \theta}{2g}$$

Question 1

A projectile is launched from the ground with an initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal, as shown in the image. What is the maximum height $$H$$ reached by the projectile? (Neglect air resistance.)

Accepted Answer

$$H = \frac{v_0$^2 \sin^2$ 	heta}{2g}$$

Question 2

A person is standing in an elevator that is moving upward at constant speed. The magnitude of the upward normal force $$N$$ exerted by the elevator floor on the person is:

Accepted Answer

$$N = W$$

Question 3

If the elevator in the previous question is now accelerating upward, how does the normal force $$N$$ compare to the weight $$W of $$the person?

Accepted Answer

$$N \u003e W$$

Question 4

In a tilted coordinate system, the acceleration vector $$\vec{a} is $$along the x-axis. The components of $$\vec{a} in $$the original (non-tilted) x-y axes are $$a_x$$ and $$a_y. $$What is the value of $$a_x$$?

Accepted Answer

$$a_x = a \cos 	heta$$

Question 5

A block of mass $$m$$ slides down a frictionless ramp inclined at an angle $$	heta to $$the horizontal. What is the acceleration of the block down the ramp?

Accepted Answer

$$a = g \sin 	heta$$

Question 6

Two blocks, A and B, are in contact on a frictionless air track as shown. A force is applied to block A, pushing both blocks to the right. How does the force that block B exerts on block A compare to the force that block A exerts on block B?

Accepted Answer

The forces are equal in magnitude and opposite in direction.

Question 7

A hockey puck is sliding on a frictionless ice rink. Three forces act on it as shown in the diagram. What is the net force on the puck?

Accepted Answer

The vector sum of all three forces.

Question 8

A velocity vs. time graph for an object is shown, with velocity increasing linearly with time. What is the acceleration of the object?

Accepted Answer

The acceleration is constant and positive.

Question 9

A mass $$m is $$pulled along a rough table at constant velocity with an external force $$F at $$some angle above the horizontal. Which equation correctly represents the y-component of Newton's 2nd law for the mass?

Accepted Answer

$$N + F \sin 	heta - mg = 0$$

Question 10

In an Atwood's machine, mass $$A is $$twice the mass of $$B$$ ($$m_A = 2m_B). $$What is the tension $$T in $$the string above mass $$A$$?

Accepted Answer

Neither of these

Question 11

A conical pendulum (tetherball) moves in a horizontal circle at constant speed. What is the direction of the net force on the ball?

Accepted Answer

Toward the center of the circle

Question 12

A block of mass $$m is at $$rest on an inclined plane with angle $$	heta$$ and coefficient of static friction $$\mu_s. $$What is the maximum value of $$	heta$$ before the block starts to slide?

Accepted Answer

$$	heta = \arctan(\mu_s)$$

Question 13

A motorcycle is turning in a circle of radius $$r on a $$flat road. The coefficient of static friction between the tires and the road is $$\mu_s. $$What is the maximum speed $$v_{max}$$ the motorcycle can have without sliding?

Accepted Answer

$$v_{max} = \sqrt{\mu_s g r}$$

Question 14

A child pulls a 5.0 kg crate across the floor with a string at a $$30^\circ$$ angle above the horizontal. The tension in the string is 17 N, and the crate accelerates at $$0.6\ \mathrm{m/s^2$}$$ horizontally. What is the correct expression for the coefficient of kinetic friction $$\mu_k$$?

Accepted Answer

$$\mu_k = \frac{T \cos 30^\circ - m a}{m g - T \sin 30^\circ}$$

Question 15

A block of mass $$m is at $$rest on a horizontal surface. Which of the following statements is true about the normal force $$N$$ acting on the block?

Accepted Answer

$$N = mg$$

Question 16

A person riding in a car during a sharp left turn feels pushed against the right side door. From the perspective of an outside (inertial) observer, what is happening?

Accepted Answer

The door is exerting a leftward force on the person.

Question 17

A block is pulled across a rough surface at constant speed. Which set of relationships is correct?

Accepted Answer

The pulling force equals the kinetic friction force.

Question 18

A mass $$m is $$attached to a string and swung in a horizontal circle of radius $$R at $$constant speed $$v. $$What is the tension $$T in $$the string (neglect gravity)?

Accepted Answer

$$T = \frac{mv^2$}{R}$$

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