Explanation Given: The weight of the crate, W = 150 lb . The force exerts on the crate, F = 100 lb f The angle at which the crate slides up the inclined plane, θ = 30 ° . The time required in sliding the crate in the upward direction, t = 4 s . The constant downward acceleration due to gravity, a y = 32.2 ft / s 2 . The initial velocity of the crate in the horizontal direction, v x = 0 . The coefficient of friction between the crate force and the ground, μ K = 0.2 . Show the free body diagram of the crate at an inclined angle of 30 ° from the ground as in Figure (1). For vertical motion of the crate Refer to Figure (1), apply the principle of impulse and momentum equation. m ( v y ) 1 + ∑ ∫ t 1 t 2 F y d t = m ( v y ) 2 W a ( v y ) 1 + N [ t ] t 1 t 2 + F sin θ [ t ] t 1 t 2 − W [ t ] t 1 t 2 = W a ( v y ) 2 (I) Here, the normal force is N , the initial and final velocity of the block in vertical upward direction is ( v y ) 1 and ( v y ) 2 respectively, initial and final linear momentum of the block is m ( v y ) 1 and m ( v y ) 2 , impulses acting on the block from time limits t 1 to t 2 is ∑ ∫ t 1 t 2 F y d t , force, and variable in time is dt . For horizontal motion of the crate Refer to Figure (1), apply the principle of impulse and momentum equation. m ( v x ) 1 + ∑ ∫ t 1 t 2 F x d t = m ( v x ) 2 W a ( v x ) 1 + F cos θ [ t ] t 1 t 2 − μ k N [ t ] t 1 t 2 = W a ( v x ) 2 (II) Here, the normal force is N , the initial and final velocity of the block in horizontal direction is ( v x ) 1 and ( v x ) 2 respectively, initial and final linear momentum of the block is m ( v x ) 1 and m ( v x ) 2 , impulses acting on the block from time limits t 1 to t 2 is ∑ ∫ t 1 t 2 F x d t , force, and variable in time is dt

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ISBN: 9780137514724

Author: HIBBELER

Publisher: PEARSON

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Chapter 15, Problem 2FP

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The speed of the crate when t reaches 4 s:

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The speed of the crate when t reaches 4 s:

Solution Summary: The author shows the free body diagram of the crate at an inclined angle of 30° from the ground as in Figure (1).

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Chapter 15 Solutions