Q: A block of mass $$m = 5.6\ \mathrm{kg} is $$pulled up a $$24^\circ$$ incline by a force $$F = 33\ \mathrm{N}$$ parallel to the incline. If the incline is frictionless, what is the acceleration of the block?

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

Q: A $$1,240\ \mathrm{N}$$ crate is pushed across a level floor at constant speed by a $$320\ \mathrm{N}$$ force at $$20.0^\circ$$ below the horizontal. What is the coefficient of kinetic friction $$\mu_k$$ between the crate and the floor?

$$\mu_k = \frac{F\cos\theta}{mg - F\sin\theta}$$

Q: A block of mass $$m is $$pulled up a rough incline of angle $$\theta$$ with coefficient of kinetic friction $$\mu_k. $$What is the net force $$F_{\mathrm{net}}$$ acting up the incline if a force $$F is $$applied parallel to the incline?

$$F_{\mathrm{net}} = F - mg\sin\theta - \mu_k mg\cos\theta$$

Question 1

A bag of rice weighs 2.00 lb on Earth. What is its mass in kilograms on the Moon, where the free-fall acceleration is one-sixth that on Earth?

Accepted Answer

$$0.907\ \mathrm{kg}$$

Question 2

A student of mass $$63.4\ \mathrm{kg}$$ slides down a $$24.2\ \mathrm{m}$$ long slide inclined at $$20.1^\circ to $$the horizontal. If the coefficient of kinetic friction is $$0.133$$, what is the force of kinetic friction acting on the student?

Accepted Answer

$$77.0\ \mathrm{N}$$

Question 3

A block of mass $$m = 5.6\ \mathrm{kg} is $$pulled up a $$24^\circ$$ incline by a force $$F = 33\ \mathrm{N}$$ parallel to the incline. If the incline is frictionless, what is the acceleration of the block?

Accepted Answer

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

Question 4

Two identical strings make an angle $$	heta = 32.3^\circ$$ with the vertical and support a block of mass $$m = 11.7\ \mathrm{kg}. $$What is the tension $$T in $$each string?

Accepted Answer

$$T = \frac{mg}{2\cos	heta}$$

Question 5

A $$1,240\ \mathrm{N}$$ crate is pushed across a level floor at constant speed by a $$320\ \mathrm{N}$$ force at $$20.0^\circ$$ below the horizontal. What is the coefficient of kinetic friction $$\mu_k$$ between the crate and the floor?

Accepted Answer

$$\mu_k = \frac{F\cos	heta}{mg - F\sin	heta}$$

Question 6

An elevator of mass $$m is $$moving upward with an acceleration $$a. $$The tension $$T in $$the cable is:

Accepted Answer

$$T = mg + ma$$

Question 7

A block of mass $$m is $$dropped from a height $$h. $$How long does it take to hit the ground? (Ignore air resistance.)

Accepted Answer

$$t = \sqrt{\frac{2h}{g}}$$

Question 8

A car of mass $$3,000\ \mathrm{kg} is $$acted on by two forces: $$F_1 = 425$$\ \mathrm{N}$$ at 10$$^\circ$$ above the forward direction and F_2$ = 366\ \mathrm{N} at$$ $$30^\circ$$ below the forward direction. What is the magnitude of the resultant force?

Accepted Answer

$$F_{\mathrm{res}} = \sqrt{(F_1$\cos\$$theta_1$$ + F_2$\cos\$$theta_2$$)^2$$ + ($$F_1$$\sin\$$theta_1$$ - $$F_2$$\sin\$$theta_2)^2$}$$

Question 9

A block of mass $$m is on a $$level surface. What is the normal force $$N$$ acting on it?

Accepted Answer

$$N = mg$$

Question 10

A block of mass $$m is on a $$surface tilted at an angle $$	heta$$ above the horizontal. What is the normal force $$N$$ acting on the block?

Accepted Answer

$$N = mg\cos	heta$$

Question 11

A $$3.00\ \mathrm{kg}$$ box starts from rest at the top of a $$36.0^\circ$$ incline and slides $$2.00\ \mathrm{m}$$ down in $$1.20\ \mathrm{s}. $$What is the magnitude of its acceleration?

Accepted Answer

$$a = \frac{2\Delta x}{t^2$}$$

Question 12

A block of mass $$m is $$pulled up a frictionless incline of angle $$	heta by a $$force $$F$$ parallel to the incline. What is the minimum value of $$F$$ required to move the block up at constant velocity?

Accepted Answer

$$F = mg\sin	heta$$

Question 13

Two objects of masses $$m_1$$ and $$m_2$$ are connected by a light string over a frictionless pulley. If $$m_2$$ \u003e $$m_1$$, what is the acceleration $$a of $$the system?

Accepted Answer

$$a = \frac{(m_2$ - m_1$)g}{m_1$ + m_2$}$$

Question 14

A block of mass $$m is $$dropped from a height $$h$$ and is subject to a constant horizontal force $$F$$ while falling. What is the horizontal acceleration $$a_x of $$the block?

Accepted Answer

$$a_x = \frac{F}{m}$$

Question 15

A $$15.2\ \mathrm{kg}$$ block is resting on the floor of an elevator accelerating downward at $$2.03\ \mathrm{m/s^2$}. $$What is the normal force $$N$$ acting on the block?

Accepted Answer

$$N = m(g - a)$$

Question 16

A crate is being pulled at constant speed by a force $$F at an $$angle $$	heta$$ above the horizontal. If the coefficient of kinetic friction is $$\mu_k$$, what is the expression for the normal force $$N$$?

Accepted Answer

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

Question 17

A block of mass $$m is $$pulled up a rough incline of angle $$	heta$$ with coefficient of kinetic friction $$\mu_k. $$What is the net force $$F_{\mathrm{net}}$$ acting up the incline if a force $$F is $$applied parallel to the incline?

Accepted Answer

$$F_{\mathrm{net}} = F - mg\sin	heta - \mu_k mg\cos	heta$$

Question 18

A $$4.20\ \mathrm{kg}$$ block on a frictionless table is connected by a string over a pulley to a $$10.5\ \mathrm{kg}$$ hanging mass. What is the tension $$T in $$the string?

Accepted Answer

$$T = \frac{m_1$ m_2$ g}{m_1$ + m_2$}$$

Forces, Newton's Laws, and Applications: Study Notes for PHYS 1114 Assignment 4

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