Explanation Given: The mass of the crate is m = 75 kg . The crate initially at rest at point ( A ) . The force acting on the crate is F = 300 N . Neglect the friction and the size of the pulley. Draw the free body diagram of the crate as shown in Figure (1). Refer figure (1). The force components N , W , R does not create any displacement of the crate. Hence the work done by these forces is zero. The force ( F ) creates the displacement of crate and causes the displacement of the crate along its direction and does positive work. From Figure (1). Write the formula for change length of the cord when the crate moves from point ( A ) to point ( B ) . s = A C − B C (I) Write the formula to calculate the work done by the force ( F ) . U F ( 1 − 2 ) = F s (II) Here, F is the force and s is the displacement. Write the formula for kinetic energy ( T ) . T = 1 2 m v 2 (III) Here, m is the mass of the object and v is the velocity of the object. Write the formula for Principle of Work and Energy. T 1 + ∑ U 1 − 2 = T 2 (IV) 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 crate. Conclusion: Refer Figure (1). Calculate the change in length of the chord when the crate moves from point ( A ) to point ( B ) . Use Pythagoras theorem to calculate A C , B C . A C = 8 2 + 6 2 B C = 2 2 + 6 2 Substitute 8 2 + 6 2 for A C and 2 2 + 6 2 for B C in Equation (I). s = 8 2 + 6 2 − 2 2 + 6 2 = 100 − 40 = 10 − 6.3245 = 3

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 14.3, Problem 39P

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The speed of the crate when it reaches the point (B) .

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Chapter 14.3, Problem 38P

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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 of the crate when it reaches the point ( B ) .

Solution Summary: The author explains how the crate's speed is determined when it reaches the point (B).

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