Q: A 250 g hockey puck is launched up a metal ramp inclined at $$40^\circ. $$The coefficients of static and kinetic friction are $$\mu_s = 0.42$$ and $$\mu_k = 0.31. If $$the puck's initial speed is $$70\ \mathrm{m/s}$$, what is the maximum vertical height it reaches above its starting point?

$$h = \frac{v_0$^2}{2g(\sin\theta + \mu_k \cos\theta)}$$

Q: A 40.0-kg object falls with air resistance proportional to its speed. If its terminal speed is $$100.0\ \mathrm{m/s}$$, what is the drag force when it is falling at $$35.0\ \mathrm{m/s}$$?

$$F_{\text{drag}} = mg \cdot \frac{v}{v_t}$$

Q: In the sixth image (block on a $$30^\circ$$ incline, horizontal force $$F$$ applied), if the block has mass $$6.00\ \mathrm{kg}$$ and the coefficient of static friction is $$0.650$$, what is the minimum horizontal force $$F$$ required to start the block moving up the incline?

$$F = mg(\sin\theta + \mu_s \cos\theta) / \cos\theta$$

Q: In the seventh image (block A on a $$30^\circ$$ incline connected to block B over a pulley), if block A has mass $$3.20\ \mathrm{kg}$$, block B has mass $$2.95\ \mathrm{kg}$$, and the coefficient of kinetic friction between A and the plane is $$0.400$$, what is the acceleration of the blocks?

$$a = \frac{m_B g - m_A g \sin\theta - \mu_k m_A g \cos\theta}{m_A + m_B}$$

Question 1

Restate Newton’s First Law of Motion and identify the conditions required for it to hold true.

Accepted Answer

An object remains at rest or in uniform motion in a straight line unless acted upon by a net external force. This law holds when the net external force is zero.

Question 2

In the system shown in the first image (blocks P and Q connected by a cord, with force $$F$$ applied to Q), if the mass of P is greater than that of Q, what is the magnitude of the force exerted by the connecting cord on body P?

Accepted Answer

Less than $$F$$ but not zero

Question 3

For the Atwood’s machine shown in the second image (masses $$M$$ and $$m$$ connected over a pulley), what is the acceleration of the system? (Assume $$M \u003e m$$ and ignore friction and pulley mass.)

Accepted Answer

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

Question 4

A 12.0-kg object is acted on by two forces. One of the forces is 20.0 N acting toward the south. If the resulting acceleration is $$2.0\ \mathrm{m/s^2$}$$ toward the south, what is the magnitude and direction of the other force?

Accepted Answer

4.0 N north

Question 5

In the third image (block A on a frictionless table connected to hanging block B), if block A has mass 7.0 kg and block B has mass 9.0 kg, what is the acceleration of block A?

Accepted Answer

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

Question 6

In the fourth image (two 1.0 kg blocks connected by two ropes, both ropes have mass 0.4 kg, assembly accelerated upward at $$2.9\ \mathrm{m/s^2$}$$), what is the tension at the top end of rope 1?

Accepted Answer

$$T = (2.8)g + (2.8)a$$

Question 7

In the fifth image (two forces $$\vec{F}_1$$ and $$\vec{F}_2 of $$equal magnitude $$3.9\ \mathrm{N} at a$$ $$50^\circ$$ angle), what third force will cause the object to be in equilibrium?

Accepted Answer

$$\vec{F}_3 = - (\vec{F}_1 + \vec{F}_2)$$

Question 8

A car travels at a steady $$50.0\ \mathrm{m/s}$$ around a horizontal curve of radius $$250\ \mathrm{m}. $$What is the minimum coefficient of static friction required between the road and the car's tires to prevent sliding?

Accepted Answer

$$\mu_s = \frac{v^2$}{rg}$$

Question 9

A 250 g hockey puck is launched up a metal ramp inclined at $$40^\circ. $$The coefficients of static and kinetic friction are $$\mu_s = 0.42$$ and $$\mu_k = 0.31. If $$the puck's initial speed is $$70\ \mathrm{m/s}$$, what is the maximum vertical height it reaches above its starting point?

Accepted Answer

$$h = \frac{v_0$^2}{2g(\sin	heta + \mu_k \cos	heta)}$$

Question 10

A 40.0-kg object falls with air resistance proportional to its speed. If its terminal speed is $$100.0\ \mathrm{m/s}$$, what is the drag force when it is falling at $$35.0\ \mathrm{m/s}$$?

Accepted Answer

$$F_{	ext{drag}} = mg \cdot \frac{v}{v_t}$$

Question 11

A 1300-kg car traveling at $$25.0\ \mathrm{m/s}$$ comes to a stop in $$555\ \mathrm{m}. $$What is the magnitude of the average braking force acting on the car?

Accepted Answer

$$F = \frac{m v^2$}{2d}$$, with direction opposite to motion

Question 12

In the sixth image (block on a $$30^\circ$$ incline, horizontal force $$F$$ applied), if the block has mass $$6.00\ \mathrm{kg}$$ and the coefficient of static friction is $$0.650$$, what is the minimum horizontal force $$F$$ required to start the block moving up the incline?

Accepted Answer

$$F = mg(\sin	heta + \mu_s \cos	heta) / \cos	heta$$

Question 13

In the seventh image (block A on a $$30^\circ$$ incline connected to block B over a pulley), if block A has mass $$3.20\ \mathrm{kg}$$, block B has mass $$2.95\ \mathrm{kg}$$, and the coefficient of kinetic friction between A and the plane is $$0.400$$, what is the acceleration of the blocks?

Accepted Answer

$$a = \frac{m_B g - m_A g \sin	heta - \mu_k m_A g \cos	heta}{m_A + m_B}$$

Question 14

In the eighth image (three masses: 1.0 kg, 2.0 kg, and 3.0 kg connected over pulleys, with the 2.0 kg block on a table with $$\mu_k = 0.28$$), what is the acceleration of the 2.0-kg block?

Accepted Answer

$$a = \frac{(m_3$ - m_1$)g - \mu_k m_2$ g}{m_1$ + m_2$ + m_3$}$$

Question 15

Which of the following best describes an action-reaction pair according to Newton’s Third Law?

Accepted Answer

The force of the Earth pulling on a falling apple and the force of the apple pulling on the Earth.

Question 16

If you increase the mass of an object but want to maintain the same acceleration, what must happen to the net force applied, according to Newton’s Second Law?

Accepted Answer

The net force must increase proportionally to the mass.

Question 17

In what way can friction help an object move, and what type of friction is responsible for this?

Accepted Answer

Static friction provides traction, allowing objects like cars to move forward.

Physics Exam 2 Study Guide: Forces, Motion, and Equilibrium

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