(a) Explanation The masses attached to the pulley move with acceleration in the direction of the heavier block. Since the smaller block is given an initial velocity in opposite direction then will move some distance in the direction opposite to the acceleration. The free body diagram for the lighter block is given as. Write the expression for the equilibrium of the block as. T − m 1 g = m 1 a (I) Here, T is the tension developed in the string, m 1 is the mass of the block, g is the acceleration due to gravity and a is the acceleration of the block. The free body diagram for the heavier block is given as. Write the expression for the equilibrium of the block as. m 2 g − T = m 2 a (II) Here, m 2 is the mass of the block and a is the acceleration of the block. Add the equation (I) and (II). T − m 1 g + m 2 g − T = m 1 a + m 2 a m 2 g − m 1 g = ( m 1 + m 2 ) a Rearrange the above expression for a . a = ( m 2 − m 1 m 1 + m 2 ) g (III) Since the lighter block has a velocity in the negative direction, it will cover some distance and then move back. Write the expression for the newton’s third equation of motion as. v 2 = u 2 + 2 a x (IV) Here, v is the final velocity of block, u is the initial velocity of the block, x is the distance covered by the block in negative direction (b) To determine The velocity of m 1 after 1.80 s .

Physics for Scientists and Engineers with Modern, Revised Hybrid (with Enhanced WebAssign Printed Access Card for Physics, Multi-Term Courses)

9th Edition

ISBN: 9781305266292

Author: Raymond A. Serway, John W. Jewett

Publisher: Cengage Learning

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Chapter 5, Problem 50P

(a)

To determine

The distance covered by m1 below its initial level.

(b)

To determine

The velocity of m1 after 1.80 s.

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Chapter 5, Problem 49P

Chapter 5, Problem 51P

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Two masses are connected by a light string that passes over a frictionless pulley, as shown below. The masses are m1 = 6.32 kg, and m2 = 7.51 kg. If the coefficient of friction between the incline and m2 is 0.232 and the angle of the incline is 35.0°, find (a) acceleration of the two masses, (b) the tension in the string, and (c) the speed of each mass 2.11 s after being released from rest. (d) Also, determine what m2 would have to be in order to have the system accelerate in the direction opposite of what you found in (a). Assume m1 stays at the same. Note: this problem needs to be done using forces and FBDs - no credit will be given for doing it any other way.

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Physics for Scientists and Engineers with Modern, Revised Hybrid (with Enhanced WebAssign Printed Access Card for Physics, Multi-Term Courses)

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The distance covered by m 1 below its initial level.

Solution Summary: The author calculates the distance covered by m_1 below its initial level. The masses attached to the pulley move with acceleration in the direction of the heavier block.