Q: Given the scenario above, what is the normal force $$N$$ acting on $$m_1$$?

$$N = m_1$ g \cos \alpha = 117.8\ \text{N}$$

Q: What is the tension $$T in $$the rope connecting $$m_1$$ and $$m_2$$ during the motion?

$$T = m_1$ a + \mu_k N + m_1$ g \sin \alpha = 257.4\ \text{N}$$

Q: What is the value of $$m_2$$ required for the system to descend as described in the problem?

$$m_2$$ = \frac{T}{g - a} = 36.0\ \text{kg}$$

Question 1

A 20.0 kg block ($$m_1) $$rests on an incline at angle $$\alpha = 53.1^\circ$$ and is connected by a rope to a hanging block ($$m_2) as $$shown. The coefficient of kinetic friction between $$m_1$$ and the incline is $$\mu_k = 0.40. If$$ $$m_2$$ descends 12.0 m in 3.00 s after release from rest, what is the acceleration of the system?

Accepted Answer

$$a = 2.67\ 	ext{m/s}^2$$

Question 2

Given the scenario above, what is the normal force $$N$$ acting on $$m_1$$?

Accepted Answer

$$N = m_1$ g \cos \alpha = 117.8\ 	ext{N}$$

Question 3

What is the tension $$T in $$the rope connecting $$m_1$$ and $$m_2$$ during the motion?

Accepted Answer

$$T = m_1$ a + \mu_k N + m_1$ g \sin \alpha = 257.4\ 	ext{N}$$

Question 4

Which equation correctly relates the acceleration $$a to $$the distance $$d$$ and time $$t$$ for the hanging block starting from rest?

Accepted Answer

$$a = \frac{2d}{t^2$}$$

Question 5

If the coefficient of kinetic friction $$\mu_k is $$increased, what happens to the required mass $$m_2$$ for the same acceleration?

Accepted Answer

The required mass $$m_2$$ increases.

Question 6

Which of the following best describes the role of friction in the motion of $$m_1 on $$the incline?

Accepted Answer

Friction opposes the motion of $$m_1$$ and increases the tension required in the rope.

Question 7

If the system is released from rest and $$m_2 is $$too small, what will happen?

Accepted Answer

$$m_1$$ will not move and the system will remain at rest.

Question 8

Which equation gives the tension $$T in $$the rope for $$m_1 on $$the incline?

Accepted Answer

$$T = m_1$ a + \mu_k N + m_1$ g \sin \alpha$$

Question 9

If the incline angle $$\alpha is $$increased, what happens to the normal force $$N on$$ $$m_1$$?

Accepted Answer

The normal force $$N$$ decreases.

Question 10

What is the value of $$m_2$$ required for the system to descend as described in the problem?

Accepted Answer

$$m_2$$ = \frac{T}{g - a} = 36.0\ 	ext{kg}$$

Question 11

If the rope connecting $$m_1$$ and $$m_2 is $$not massless, how would this affect the calculations?

Accepted Answer

The mass of the rope would need to be included in the equations for both tension and acceleration.

Question 12

Which of the following is NOT a valid assumption for solving this problem?

Accepted Answer

The tension in the rope is different for $$m_1$$ and $$m_2.$$

Solving a Two-Block System with Friction and Inclined Plane

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