Q: A $$6.0\ \mathrm{kg}$$ box slides down a $$39^\circ$$ incline with a coefficient of kinetic friction $$\mu_k = 0.19. $$What is the acceleration of the box down the slope?

$$a = g \sin \theta - \mu_k g \cos \theta$$

Q: A $$200\ \mathrm{g}$$ hockey puck is launched up a $$30^\circ$$ ramp with $$\mu_k = 0.30$$ and initial speed $$4.9\ \mathrm{m/s}. $$What speed does it have when it returns to its starting point?

$$v = \sqrt{v_0$^2 - 2 \mu_k g d \cos \theta}$$

Q: A $$50.0\ \mathrm{kg}$$ block is pulled up a $$16.0^\circ$$ slope by a $$250\ \mathrm{N}$$ force parallel to the slope. The coefficient of kinetic friction is $$0.200. $$What is the acceleration of the block?

$$a = \dfrac{F - mg \sin \theta - \mu_k mg \cos \theta}{m}$$

Q: A block is given a brief push up a $$20.0^\circ$$ frictionless incline with initial speed $$12.0\ \mathrm{m/s}. $$How far along the incline does it travel before coming to rest?

$$d = \dfrac{v_0$^2}{2g \sin \theta}$$

Question 1

Refer to the first image. Two masses, $$M = 0.60\ \mathrm{kg}$$ and $$m = 0.40\ \mathrm{kg}$$, are connected by a light string over a frictionless, massless pulley. What is the magnitude of the acceleration of the system after release?

Accepted Answer

$$a = \dfrac{(M - m)g}{M + m}$$

Question 2

In the system shown in the first image, what is the tension $$T in $$the string connecting the two masses?

Accepted Answer

$$T = \dfrac{2Mm}{M + m}g$$

Question 3

Refer to the second image. Two $$1.0\ \mathrm{kg}$$ blocks are connected by two ropes (each $$0.25\ \mathrm{kg}) $$and are accelerated upward at $$2.3\ \mathrm{m/s^2$} by a $$force $$\vec{F}. $$What is the tension at the top end of Rope 1?

Accepted Answer

$$T = (2.0 + 0.5)g + (2.0 + 0.5)a$$

Question 4

In the third image, block A ($$4.0\ \mathrm{kg}) $$slides on a frictionless table and is connected by a string and pulley to a hanging block B ($$5.0\ \mathrm{kg}). $$What is the acceleration of block A?

Accepted Answer

$$a = \dfrac{m_B g}{m_A + m_B}$$

Question 5

Refer to the fourth image. A $$6.00\ \mathrm{kg}$$ block is pushed by a $$20.0\ \mathrm{N}$$ force and is in contact with a $$4.00\ \mathrm{kg}$$ block on a frictionless surface. What is the force that the $$6.00\ \mathrm{kg}$$ block exerts on the $$4.00\ \mathrm{kg}$$ block?

Accepted Answer

$$8.00\ \mathrm{N}$$

Question 6

In the fifth image, a $$9.0\ \mathrm{kg}$$ block accelerates downward, pulling two blocks ($$6.0\ \mathrm{kg}$$ and $$4.0\ \mathrm{kg}) up a$$ $$30^\circ$$ incline. What is the tension in the rope connecting the $$6.0\ \mathrm{kg}$$ and $$4.0\ \mathrm{kg}$$ blocks?

Accepted Answer

$$33\ \mathrm{N}$$

Question 7

Refer to the sixth image. A $$3.00\ \mathrm{kg}$$ block sits atop a $$4.00\ \mathrm{kg}$$ block. The coefficient of static friction between all surfaces is $$0.800. $$What horizontal force $$F$$ must be applied to the $$4.00\ \mathrm{kg}$$ block to make it move?

Accepted Answer

$$54.9\ \mathrm{N}$$

Question 8

In the seventh image, box A ($$8.0\ \mathrm{kg}) is on a $$table with kinetic friction $$\mu_k = 0.10$$ and is connected by a cord over a pulley to box B ($$15.0\ \mathrm{kg}) $$hanging off the edge. What is the acceleration of the system?

Accepted Answer

$$a = \dfrac{m_B g - \mu_k m_A g}{m_A + m_B}$$

Question 9

Refer to the eighth image. A $$4.00\ \mathrm{kg}$$ box sits atop a $$10.0\ \mathrm{kg}$$ box. The coefficient of kinetic friction between all surfaces is $$0.600. If a$$ $$150.0\ \mathrm{N}$$ horizontal pull is exerted on the lower box and the boxes move together, what is the friction force on the upper box?

Accepted Answer

$$19.3\ \mathrm{N}$$\ to\ the\ right$

Question 10

A $$23\ \mathrm{kg}$$ mass is connected to a nail on a frictionless table by a massless string $$1.3\ \mathrm{m}$$ long. If the tension in the string is $$51\ \mathrm{N}$$ while the mass moves in a uniform circle, how long does it take for the mass to make one complete revolution?

Accepted Answer

$$T = 2\pi \sqrt{\dfrac{m r}{F_T}}$$

Question 11

A car travels at a steady $$40.0\ \mathrm{m/s}$$ around a horizontal curve of radius $$200\ \mathrm{m}. $$What is the minimum coefficient of static friction required to prevent sliding?

Accepted Answer

$$\mu_s = \dfrac{v^2$}{r g}$$

Question 12

A $$6.0\ \mathrm{kg}$$ box slides down a $$39^\circ$$ incline with a coefficient of kinetic friction $$\mu_k = 0.19. $$What is the acceleration of the box down the slope?

Accepted Answer

$$a = g \sin 	heta - \mu_k g \cos 	heta$$

Question 13

A $$200\ \mathrm{g}$$ hockey puck is launched up a $$30^\circ$$ ramp with $$\mu_k = 0.30$$ and initial speed $$4.9\ \mathrm{m/s}. $$What speed does it have when it returns to its starting point?

Accepted Answer

$$v = \sqrt{v_0$^2 - 2 \mu_k g d \cos 	heta}$$

Question 14

A $$50.0\ \mathrm{kg}$$ block is pulled up a $$16.0^\circ$$ slope by a $$250\ \mathrm{N}$$ force parallel to the slope. The coefficient of kinetic friction is $$0.200. $$What is the acceleration of the block?

Accepted Answer

$$a = \dfrac{F - mg \sin 	heta - \mu_k mg \cos 	heta}{m}$$

Question 15

A block is given a brief push up a $$20.0^\circ$$ frictionless incline with initial speed $$12.0\ \mathrm{m/s}. $$How far along the incline does it travel before coming to rest?

Accepted Answer

$$d = \dfrac{v_0$^2}{2g \sin 	heta}$$

Question 16

A car enters a $$300\ \mathrm{m}$$ radius curve on a rainy day with $$\mu_s = 0.600. $$What is the maximum speed it can travel without sliding?

Accepted Answer

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

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