A simple Atwood machine consists of two masses m 1 and m 2 that are connected by

Question

A simple Atwood machine consists of two masses m1 and m2 that are connected by a string wound over a pulley, as seen in the figure below. Assume m2 is larger than m1. Motion in the upward direction is positive. On a piece of paper, draw two free body diagrams; one for each of the masses, showing all forces acting on each mass. Then answer the following questions.

(a) Identify the forces acting on the mass m1. (Select all that apply.)

(b) Using the direction rosette indicate the direction for each of the forces acting on m1 that you identified in part (a). If any of the forces listed below is not applicable, choose 'NA'.

(c) Identify the forces acting on the mass m2. (Select all that apply.)

m1am2am1gm2g(m1 + m2)a(m1 + m2)gfTFN

(d) Using the direction rosette indicate the direction for each of the forces acting on m2 that you identified in part (c). If any of the forces listed below is not applicable, choose 'NA'.

(e) Write Newton's Second Law equation (in the form Fnet = ma) for m1 in the y-direction. It is important to use the correct signs for each of the forces. Motion in the upward direction is positive and motion in the downward direction is negative. (Be sure to enter your answer in the above form with the sum of the forces in the left hand side answer box. The right hand side answer box should have the appropriate form of ma. Use the following as necessary: a, f, FN, g, m1, and T.)

(f) Write Newton's Second Law equation (in the form Fnet = ma) for m2 in the y-direction. It is important to use the correct signs for each of the forces. Motion in the upward direction is positive and motion in the downward direction is negative. (Be sure to enter your answer in the above form with the sum of the forces in the left hand side answer box. The right hand side answer box should have the appropriate form of ma. Use the following as necessary: a, f, FN, g, m2, and T.)

(g) Use your answers from parts (e) and (f) to get an expression for the magnitude of the tension T. (Use the following as necessary:m1, m2, and g.)
T =  

(h) Use your answers from parts (e), (f), and (g) to find the magnitude of a, the acceleration of the system. (Use the following as necessary: m1, m2, and g.)
a =  

(i) In what direction will each mass accelerate?

(j) Suppose m1 = 7 kg and m2 = 11 kg. What is the tension in the string?
T =  

(k) Suppose m1 = 7 kg and m2 = 11 kg. What is the value of the acceleration?
a =  

(l) Suppose that m2 starts from rest at a height of 5 m. Use the kinematic equations to determine how long it takes for m2 to hit the ground.

Force Direction m1a ---Select--- 1 2 3 4 5 6 7 8 NA m2a ---Select--- 1 2 3 4 5 6 7 8 NA m1g ---Select--- 1 2 3 4 5 6 7 8 NA m2g ---Select--- 1 2 3 4 5 6 7 8 NA (m1 + m2)a ---Select--- 1 2 3 4 5 6 7 8 NA (m1 + m2)g ---Select--- 1 2 3 4 5 6 7 8 NA f ---Select--- 1 2 3 4 5 6 7 8 NA T ---Select--- 1 2 3 4 5 6 7 8 NA FN ---Select--- 1 2 3 4 5 6 7 8 NA

Explanation / Answer

a) Tension and gravity force m1g

b)m1g and T

c) the tension and gravity force m2g

d) m2g and T

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