Q: A 1000 kg elevator accelerates upward at $$1.0\ \mathrm{m/s^2$}$$ for $$10\ \mathrm{m}$$, starting from rest. What is the work done by gravity on the elevator?

$$-9.8 \times 10^4$\ \mathrm{J}$$

Q: A block of mass $$m is $$pushed up a frictionless slope of angle $$\theta by a $$horizontal force $$F. $$What is the expression for the crate's speed $$v$$ when it is at height $$h$$ above the bottom of the slope?

$$v = \sqrt{\frac{2Fh}{m\sin\theta} - 2gh}$$

Q: A 1500 kg car drives off a 30-m-high cliff at $$20\ \mathrm{m/s} up a$$ $$20^\circ$$ incline. What is the time it takes to hit the ground?

$$t = \frac{v_0$\sin\theta + \sqrt{(v_0$\sin\$$theta)^2$$ + 2gh}}{g}$$

Q: A block of mass $$m$$ rests on a $$20^\circ$$ slope. It is connected by a string over a pulley to a hanging $$2.0\ \mathrm{kg}$$ mass. The coefficients of friction are $$\mu_s = 0.80$$ and $$\mu_k = 0.50. $$What is the minimum mass $$m$$ that will stick and not slip?

$$m = \frac{m_2$ - \mu_s m_2$ \cos\theta}{\sin\theta + \mu_s \cos\theta}$$

Q: Three masses (100 g, 200 g, 100 g) are connected by massless rods in a triangle. What is the $$x-$$coordinate of the center of mass if the vertices are at $$(0,0)$$, $$(0,10)$$, and $$(12,0) cm$$?

$$x_{cm} = \frac{0.1 \times 0 + 0.2 \times 0 + 0.1 \times 0.12}{0.1 + 0.2 + 0.1} = 0.06\ \mathrm{m}$$

Q: A 1000 kg elevator accelerates upward at $$1.0\ \mathrm{m/s^2$}$$ for $$10\ \mathrm{m}$$, starting from rest. What is the elevator's kinetic energy after traveling $$10\ \mathrm{m}$$?

$$1.0 \times 10^4$\ \mathrm{J}$$

Question 1

A 1000 kg elevator accelerates upward at $$1.0\ \mathrm{m/s^2$}$$ for $$10\ \mathrm{m}$$, starting from rest. What is the work done by gravity on the elevator?

Accepted Answer

$$-9.8 	imes 10^4$\ \mathrm{J}$$

Question 2

A block of mass $$m is $$pushed up a frictionless slope of angle $$	heta by a $$horizontal force $$F. $$What is the expression for the crate's speed $$v$$ when it is at height $$h$$ above the bottom of the slope?

Accepted Answer

$$v = \sqrt{\frac{2Fh}{m\sin	heta} - 2gh}$$

Question 3

A 200 g block is launched by a spring (k = 1000 N/m, compressed 15 cm) up a 45° incline (2.0 m long) with kinetic friction $$\mu_k = 0.20. $$What is the block's speed as it leaves the spring?

Accepted Answer

$$8.09\ \mathrm{m/s}$$

Question 4

A ball is thrown toward a cliff with a speed of $$30\ \mathrm{m/s} at an $$angle of $$60^\circ$$ above horizontal. It lands on the edge of the cliff $$4.0\ \mathrm{s}$$ later. What is the vertical component of the ball's initial velocity?

Accepted Answer

$$v_{0y} = 30\sin(60^\circ) = 25.98\ \mathrm{m/s}$$

Question 5

A 1500 kg car drives off a 30-m-high cliff at $$20\ \mathrm{m/s} up a$$ $$20^\circ$$ incline. What is the time it takes to hit the ground?

Accepted Answer

$$t = \frac{v_0$\sin	heta + \sqrt{(v_0$\sin\$$theta)^2$$ + 2gh}}{g}$$

Question 6

A block of mass $$m$$ rests on a $$20^\circ$$ slope. It is connected by a string over a pulley to a hanging $$2.0\ \mathrm{kg}$$ mass. The coefficients of friction are $$\mu_s = 0.80$$ and $$\mu_k = 0.50. $$What is the minimum mass $$m$$ that will stick and not slip?

Accepted Answer

$$m = \frac{m_2$ - \mu_s m_2$ \cos	heta}{\sin	heta + \mu_s \cos	heta}$$

Question 7

A 100 kg student is launched by a spring ($$k = 80,000\ \mathrm{N/m}$$, $$x_0 = 0.5$$\ \mathrm{m}$$) up a 30$$^\circ$$ incline with $$\mu_k = 0.15$$. What is the student's speed just after losing contact with the spring?

Accepted Answer

$$v = \sqrt{\frac{80,000}{100} (0.5)^2$}$$

Question 8

Three masses (100 g, 200 g, 100 g) are connected by massless rods in a triangle. What is the $$x-$$coordinate of the center of mass if the vertices are at $$(0,0)$$, $$(0,10)$$, and $$(12,0) cm$$?

Accepted Answer

$$x_{cm} = \frac{0.1 	imes 0 + 0.2 	imes 0 + 0.1 	imes 0.12}{0.1 + 0.2 + 0.1} = 0.06\ \mathrm{m}$$

Question 9

A white ball traveling at $$2.0\ \mathrm{m/s}$$ hits an equal-mass red ball at rest. The white ball is deflected by $$25^\circ$$ and slowed to $$1.5\ \mathrm{m/s}. $$What is the final speed of the red ball?

Accepted Answer

$$v = 0.90\ \mathrm{m/s}$$

Question 10

A system consists of three balls of clay (20 g, 30 g, 20 g) moving north, west, and southeast, respectively. After a perfectly inelastic collision, what is the magnitude of the final velocity?

Accepted Answer

$$v_f = 0.85\ \mathrm{m/s}$$

Question 11

A block is launched by a spring up a frictionless incline. The spring constant is $$k$$, the block mass is $$m$$, and the spring is compressed by $$x_0. $$What is the block's speed as it leaves the spring?

Accepted Answer

$$v = \sqrt{\frac{k}{m}x_0$^2}$$

Question 12

A 1000 kg elevator accelerates upward at $$1.0\ \mathrm{m/s^2$}$$ for $$10\ \mathrm{m}$$, starting from rest. What is the elevator's kinetic energy after traveling $$10\ \mathrm{m}$$?

Accepted Answer

$$1.0 	imes 10^4$\ \mathrm{J}$$

Question 13

A velocity-time graph for a particle is a straight line from $$v = 4\ \mathrm{m/s} at$$ $$t = 0 to$$ $$v = 0 at$$ $$t = 3\ \mathrm{s}. $$What is the acceleration at $$t = 3.0\ \mathrm{s}$$?

Accepted Answer

$$a = -\frac{4}{3}\ \mathrm{m/s^2$}$$

Question 14

A block of mass $$m is $$pushed up a frictionless slope of angle $$	heta by a $$horizontal force $$F. $$What is the minimum value of $$F$$ required to move the block up the slope?

Accepted Answer

$$F = mg\sin	heta + mg\cos	heta$$

Question 15

A 200 g block is launched by a spring (k = 1000 N/m, compressed 15 cm) up a 45° incline (2.0 m long) with kinetic friction $$\mu_k = 0.20. $$What is the distance $$d$$ the block sails through the air?

Accepted Answer

$$d = 6.7\ \mathrm{m}$$

Question 16

A 100 kg student is launched by a spring ($$k = 80,000\ \mathrm{N/m}$$, $$x_0 = 0.5$$\ \mathrm{m}$$) up a 30$$^\circ$$ incline with $$\mu_k = 0.15$$. How far up the incline does the student go?

Accepted Answer

$$32\ \mathrm{m}$$

Physics College Course Review: Kinematics, Dynamics, Energy, and Momentum

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