Q: A horizontal force $F$ acts on a block of mass $m$ sliding down a frictionless incline of length $L$ at angle $\theta$. What is the final speed $v_f$ of the block at the bottom?

$v_f = \sqrt{2gL\sin\theta - \frac{2F L \cos\theta}{m}}$

Question 1

A block of mass $m$ slides on a frictionless horizontal surface and compresses a spring with spring constant $k$ by a distance $x$. If the block was initially moving at speed $v_0$, what is the maximum compression $x_{max}$ of the spring?

Accepted Answer

$x_{max} = \sqrt{\frac{mv_0^2}{k}}$

Question 2

A 2 kg block slides across a rough surface with a coefficient of kinetic friction $\mu_k = 0.2$ for a distance of 5 m before coming to rest. What is the work done by friction?

Accepted Answer

$-19.6$ J

Question 3

A spring with spring constant $k = 500$ N/m is compressed by 0.2 m. What is the potential energy stored in the spring?

Accepted Answer

$10$ J

Question 4

A 1 kg ball is dropped from a height of 5 m. What is its speed just before hitting the ground? (Assume $g = 9.8$ m/s$^2$)

Accepted Answer

$9.9$ m/s

Question 5

A 3 kg object is pushed up a frictionless incline of length 4 m at an angle of $30^\circ$ to the horizontal. What is the work done by gravity?

Accepted Answer

$-58.8$ J

Question 6

A 5 kg block slides down a 2 m long slide inclined at $45^\circ$ to the horizontal. What is its speed at the bottom, neglecting friction?

Accepted Answer

$6.26$ m/s

Question 7

A horizontal force $F$ acts on a block of mass $m$ sliding down a frictionless incline of length $L$ at angle $	heta$. What is the final speed $v_f$ of the block at the bottom?

Accepted Answer

$v_f = \sqrt{2gL\sin	heta - \frac{2F L \cos	heta}{m}}$

Question 8

A 1000 kg car moving at 20 m/s collides with a stationary 4000 kg truck. After the collision, the car moves at 10 m/s at $45^\circ$ to its original direction. What is the magnitude of the truck's velocity after the collision?

Accepted Answer

$5.7$ m/s

Question 9

A ball of mass 0.5 kg is hit so that its velocity changes from 2 m/s to 8 m/s over 0.3 s. What is the average force exerted on the ball?

Accepted Answer

$10$ N

Question 10

Which of the following statements about work and energy is TRUE?

Accepted Answer

Work done by gravity is zero if displacement is perpendicular to gravity.

Question 11

A projectile is launched with total energy $E = 5$ J. At a certain point, its kinetic energy is 4 J. What is its potential energy at that point?

Accepted Answer

$1$ J

Question 12

A 15 kg child slides down a slide of length 3 m inclined at $30^\circ$ to the horizontal. What is the final speed at the bottom, neglecting friction?

Accepted Answer

$6.7$ m/s

Question 13

A 10 kg box is pulled 5 m across a horizontal floor by a force of 30 N at $30^\circ$ above the horizontal. What is the work done by the force?

Accepted Answer

$75$ J

Question 14

A 2 kg object is dropped from rest from a height of 10 m. What is its kinetic energy just before hitting the ground?

Accepted Answer

$98$ J

Question 15

A spring with $k = 100$ N/m is stretched by 0.5 m. What is the force exerted by the spring?

Accepted Answer

$50$ N$

Question 16

A 1 kg ball is thrown vertically upward with an initial speed of 10 m/s. What is its maximum height?

Accepted Answer

$5.1$ m

Question 17

A 2 kg block is attached to a spring and oscillates with amplitude 0.3 m and spring constant $k = 200$ N/m. What is its maximum speed?

Accepted Answer

$4.24$ m/s

Question 18

A 0.5 kg ball moving at 4 m/s collides elastically with a stationary 0.5 kg ball. What is the velocity of the first ball after the collision?

Accepted Answer

$0$ m/s

Question 19

A 3 kg block is pulled at constant speed across a rough surface by a force of 15 N. If the coefficient of kinetic friction is $\mu_k = 0.5$, what is the work done by friction over 4 m?

Accepted Answer

$-60$ J

Work, Energy, and Momentum in Classical Mechanics

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