Explanation Given: The mass of the block is 10 kg The force acting on the block is F = 6 N (horizontal). If the observer A is in a fixed frame x , the initial speed of the block is 5 m/s and it travels to the distance of 10 m . If the observer B is in a fixed frame x ' , the observer B moving at a constant speed of 2 m/s relative to observer A . Write the formula for work done by the force on the block. U F ( 1 − 2 ) = F s (I) Here, F is the force and s is the displacement. Write the formula for Principle of Work and Energy. T 1 + ∑ U 1 − 2 = T 2 (II) 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 block. 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 position of the block at constant acceleration. s = s 0 + v 0 t + 1 2 a c t 2 (IV) Here, s is final position, s 0 is initial position, v 0 is initial velocity, a c is constant acceleration and t is time. Conclusion: By the observer A : Calculate the Work done on the block by the force ( F ) . Substitute 6 for F and 10 for s in Equation (I). U F ( 1 − 2 ) = 6 ( 10 ) = 60 J Calculate the initial and final kinetic energy of the block. At initial: Substitute T 1 for T , 10 for m and 5 m/s for v in Equation (III). T 1 = 1 2 ( 10 ) ( 5 ) 2 = 5 ( 25 ) = 125 J At final: Substitute T 2 for T , 10 for m and v 2 for v in Equation (III). T 2 = 1 2 ( 10 ) ( v 2 ) 2 = 5 v 2 2 Calculate total work done on the block ( ∑ U 1 − 2 ) . ∑ U 1 − 2 = U F ( 1 − 2 ) Substitute 60 J for U F R ( 1 − 2 ) . ∑ U A − B = 60 J Calculate the final velocity. Substitute 125 for T 1 , 60 for ∑ U A − B and 5 v 2 2 for T 2 in Equation (III). 125 + 60 = 5 v 2 2 v 2 2 = 185 5 v 2 = 37 . v 2 = 6.083 m/s Thus, the velocity of the block in view of observer A is 6.083 m/s . By the observer B : Calculate the final velocity of the block by the observation of observer B . When the observer B moves at the constant velocity of 2 m/s in relation to observer A . The acceleration of the block is a = F m . Substitute 6 for F and 10 for m . a = 6 10 = 0.6 m/s 2 Calculate the time of the block when it is at the position of 10 m . Substitute 10 for s , 0 for s 0 , 5 for v 0 and 0.6 for a c in Equation (IV)

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ISBN: 9780137514724

Author: HIBBELER

Publisher: PEARSON

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Chapter 14, Problem 7P

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The final speed of the block by the observers A and B .

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The final speed of the block by the observers A and B .

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Chapter 14 Solutions