Q: A $$4.00\ \mathrm{kg}$$ block is pulled up a frictionless $$33.0^\circ$$ incline by a $$25.0\ \mathrm{N}$$ force that makes an angle of $$18^\circ$$ above the surface of the incline. What is the acceleration of the block?

$$a = \frac{F \cos \theta - mg \sin \alpha}{m}$$

Q: A $$5.0\ \mathrm{kg}$$ box is pulled across a horizontal surface with a force of $$20\ \mathrm{N} at$$ $$30^\circ$$ above the horizontal. If $$\mu_k = 0.2$$, what is the acceleration of the box? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

$$a = \frac{20 \cos 30^\circ - 0.2 (5.0 \times 9.8 - 20 \sin 30^\circ)}{5.0}$$

Q: A block of mass $$m is on a $$rough incline of angle $$\theta$$ with coefficient of kinetic friction $$\mu_k. $$What is the acceleration of the block down the incline?

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

Q: In a two-mass system with a frictionless pulley, if Object L ($$2.7\ \mathrm{kg}) is on a$$ $$30^\circ$$ incline and Object R ($$3.7\ \mathrm{kg}) $$hangs vertically, what is the tension in the string if the system accelerates at $$1.35\ \mathrm{m/s^2$}$$?

$$T = m_R g - m_R a = 3.7 \times 9.8 - 3.7 \times 1.35$$

Question 1

A collection of beakers is sitting on a flat table cloth. The glass beakers have a coefficient of kinetic friction $$\mu_k$$ with the table cloth. If the table cloth is jerked quickly to the right and slips out from under the beakers, what is the primary reason the beakers remain nearly stationary while the table cloth slides out from underneath them?

Accepted Answer

The inertia of the beakers resists the sudden motion, so they tend to remain at rest as the table cloth moves.

Question 2

A skier finds herself going up a small $$20.0^\circ$$ incline after building speed down a long slope. If $$\mu = 0.10 on $$the snow, what is the net force of acceleration acting on the skier as she moves up the incline?

Accepted Answer

$$a = g(\sin 20^\circ - \mu \cos 20^\circ)$$

Question 3

In a frictionless pulley system, a blue object of mass $$2.4\ \mathrm{kg} is in $$equilibrium. If the green object is raised $$12\ \mathrm{cm}$$, how far up would the blue object go?

Accepted Answer

$$6\ \mathrm{cm}$$

Question 4

A $$4.00\ \mathrm{kg}$$ block is pulled up a frictionless $$33.0^\circ$$ incline by a $$25.0\ \mathrm{N}$$ force that makes an angle of $$18^\circ$$ above the surface of the incline. What is the acceleration of the block?

Accepted Answer

$$a = \frac{F \cos 	heta - mg \sin \alpha}{m}$$

Question 5

In a two-mass system on a frictionless incline connected by a string over a pulley, Object L ($$2.70\ \mathrm{kg}) is on a$$ $$30.0^\circ$$ incline and Object R ($$3.70\ \mathrm{kg}) $$hangs vertically. If the system is released from rest, which direction will the system move?

Accepted Answer

Object L moves down the incline and Object R moves up.

Question 6

If the coefficient of kinetic friction between a block and a table is $$\mu_k$$, and the block is pulled with a force $$F at an $$angle $$	heta$$ above the horizontal, what is the expression for the normal force $$N$$ acting on the block?

Accepted Answer

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

Question 7

A $$5.0\ \mathrm{kg}$$ box is pulled across a horizontal surface with a force of $$20\ \mathrm{N} at$$ $$30^\circ$$ above the horizontal. If $$\mu_k = 0.2$$, what is the acceleration of the box? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$a = \frac{20 \cos 30^\circ - 0.2 (5.0 	imes 9.8 - 20 \sin 30^\circ)}{5.0}$$

Question 8

A $$3.0\ \mathrm{kg}$$ object is suspended from a frictionless pulley and is in equilibrium with a $$2.0\ \mathrm{kg}$$ object on the other side. If the $$2.0\ \mathrm{kg}$$ object is raised by $$10\ \mathrm{cm}$$, how far does the $$3.0\ \mathrm{kg}$$ object move?

Accepted Answer

$$5\ \mathrm{cm}$$

Question 9

A block of mass $$m is on a $$rough incline of angle $$	heta$$ with coefficient of kinetic friction $$\mu_k. $$What is the acceleration of the block down the incline?

Accepted Answer

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

Question 10

A $$4.0\ \mathrm{kg}$$ block is pulled up a $$33.0^\circ$$ frictionless incline by a $$25.0\ \mathrm{N}$$ force at $$18^\circ$$ above the incline. What is the component of the pulling force parallel to the incline?

Accepted Answer

$$25.0 \cos 18^\circ$$

Question 11

If a tablecloth is pulled slowly from under a set of beakers, what is most likely to happen to the beakers?

Accepted Answer

They will move with the tablecloth due to friction.

Question 12

A $$2.0\ \mathrm{kg}$$ block is on a $$30^\circ$$ incline with $$\mu_k = 0.15. $$What is the frictional force acting on the block?

Accepted Answer

$$f_k = \mu_k mg \cos 30^\circ$$

Question 13

In a two-mass system with a frictionless pulley, if Object L ($$2.7\ \mathrm{kg}) is on a$$ $$30^\circ$$ incline and Object R ($$3.7\ \mathrm{kg}) $$hangs vertically, what is the tension in the string if the system accelerates at $$1.35\ \mathrm{m/s^2$}$$?

Accepted Answer

$$T = m_R g - m_R a = 3.7 	imes 9.8 - 3.7 	imes 1.35$$

Question 14

A skier is moving up a $$20^\circ$$ incline with a coefficient of friction $$\mu = 0.10. $$Which of the following best describes the net force acting on the skier?

Accepted Answer

The net force is the sum of the downslope component of gravity and the frictional force.

Question 15

If a block is pulled at constant velocity across a horizontal surface, what is the relationship between the pulling force $$F$$ and the frictional force $$f_k$$?

Accepted Answer

$$F = f_k$$

Question 16

A $$4.0\ \mathrm{kg}$$ block is pulled up a $$33.0^\circ$$ frictionless incline by a $$25.0\ \mathrm{N}$$ force at $$18^\circ$$ above the incline. What is the net force acting on the block along the incline?

Accepted Answer

$$F_{	ext{net}} = 25.0 \cos 18^\circ - 4.0 	imes 9.8 \sin 33^\circ$$

Question 17

A $$2.0\ \mathrm{kg}$$ block is on a $$30^\circ$$ incline with $$\mu_k = 0.15. $$What is the acceleration of the block down the incline?

Accepted Answer

$$a = 9.8 (\sin 30^\circ - 0.15 \cos 30^\circ)$$

Review Problems: Ramps, Pulleys, and No-Mass Systems (Unit 4)

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드