Explanation Given: The mass of the collar is 10 lb . The force acting on the collar via cord is F = 30 lb . Neglect the size of the pulley. Draw the free body diagram of the collar as shown in Figure (1). Refer figure (1b). The force component N does not create any displacement of the collar. Hence the work done by these forces is zero. The force ( W ) acts in opposite direction to the displacement of collar and does negative work. The force ( F ) creates the displacement of collar and causes the displacement of the collar along its direction and does positive work. From Figure (1). Write the formula for change length of the cord when the collar moves from point ( A ) to point ( B ) . s = A C − B C (I) Write the formula to calculate the work done by the weight of the collar ( W ) . U W ( A − B ) = W s (II) Here, W is the weight of the collar and s is the displacement. Write the formula to calculate the work done by the force ( F ) . U F ( A − B ) = F s (III) Here, F is the force. Write the formula for kinetic energy ( T ) . T = 1 2 m v 2 (IV) Here, m is the mass of the object and v is the velocity of the collar. Write the formula for Principle of Work and Energy. T 1 + ∑ U 1 − 2 = T 2 (V) Here, T 1 is initial kinetic energy, T 2 is final kinetic energy and ∑ U 1 − 2 is total work done by all the forces on the collar. Conclusion: Refer Figure (1a). Calculate the change in length of the chord when the collar moves from point ( A ) to point ( B ) due to force ( F ) . Use Pythagoras theorem to calculate A C . A C = 6 2 + 4.5 2 ft Substitute 6 2 + 4.5 2 ft for A C and 2 ft for B C in Equation (I). s = 6 2 + 4.5 2 ft − 2 ft = 56.25 − 2 = 7.5 − 2 = 5.5 ft Calculate the work done by weight of the collar ( W ) . From Figure (1a). The vertical displacement of collar from point A to B is 4.5 ft . Substitute 10 lb for W and 4.5 ft for s in Equation (II). U W ( A − B ) = 10 lb ( 4.5 ft ) = 45 ft ⋅ lb Calculate the work done by the force ( F )

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 14.3, Problem 17P

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Chapter 14 Solutions

Engineering Mechanics: Statics & Dynamics (14th Edition)

Ch. 14.3 - Determine the work of the force when it displaces...Ch. 14.3 - Determine the kinetic energy of the 10-kg block.Ch. 14.3 - Prob. 1FP Ch. 14.3 - If the motor exerts a constant force of 300 N on...Ch. 14.3 - If the motor exerts a force of F = (600 + 2s2) N...Ch. 14.3 - The 1.8-Mg dragster is traveling at 125 m/s when...Ch. 14.3 - When s = 0.5 m, the spring is unstretched and the...Ch. 14.3 - The 5-lb collar is pulled by a cord that passes...Ch. 14.3 - The 20-kg crate is subjected to a force having a...Ch. 14.3 - Prob. 2P

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The speed when the collar when it passes the point ( B ) .

Solution Summary: The author illustrates how the force component N acts in opposite direction to the displacement of the collar and does positive work.

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