(a) Explanation Given information: The weight of the hammer ( W ) is 1.5 lb . The velocity of the hammer ( v H ) is 20 ft/s . The acceleration due to gravity ( g ) is 32.2 ft / s 2 . Calculation: Show the free body momentum diagram of the hammer head and anvil as Figure (1). Use the principle of conservation of momentum to the impact of hammer head and anvil, to obtain the final velocity of anvil and hammer after the impact. The expression for the principle of conservation of momentum as follows; m H v H + m A v A = m H v 2 + m A v 2 Initially the anvil is at rest, so the velocity will be zero. Substitute 0 for v A . m H v H + 0 = ( m H + m A ) v 2 v 2 = m H v H m H + m A (1) Show the free body impulse-momentum diagram of the hammer head as in Figure (2). Use the principle of the impulse momentum to the hammer head to find the impulse exerted ( F Δ t ) on the rivet. The expression for the principle of the impulse momentum as follows; m H v H − F Δ t = m H v 2 F Δ t = m H ( v H − v 2 ) (2) Calculate the mass of the hammer ( m H ) using the formula: m H = W H g Substitute 1.5 lb for W H , and 32.2 ft / s 2 for g . m H = 1.5 lb 32.2 ft / s 2 = 0.04658 lb . s 2 / ft The expression for the kinetic energy of the hammer before impact ( T 1 ) as follows; T 1 = 1 2 m H v H 2 Substitute 0.04658 lb . s 2 / ft for m H , and 20 ft / s for v H . T 1 = 1 2 m H v H 2 = 1 2 ( 0.04658 lb . s 2 / ft ) ( 20 ft / s ) 2 = ( 0.02329 ) ( 400 ) = 9.316 ft .lb Calculate the final kinetic energy of the hammer and anvil system after the impact ( T 2 ) using the formula: T 2 = 1 2 ( m H + m A ) v 2 2 Substitute m H v H m H + m A for v 2 . T 2 = 1 2 ( m H + m A ) ( m H v H m H + m A ) 2 = 1 2 m H 2 v H 2 m H + m A = 1 2 ( m H v H 2 ) ( m H m H + m A ) Substitute T 1 for 1 2 m H v H 2 (b) To determine Find the impulsive force ( F Δ t ) and the energy absorbed ( Δ T ) by the rivet which has weight of 9 lb .

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Author: BEER

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Chapter 13.3, Problem 13.148P

(a)

To determine

Find the impulsive force FΔt and the energy absorbed (ΔT) by the rivet which has infinite mass.

(b)

To determine

Find the impulsive force (FΔt) and the energy absorbed (ΔT) by the rivet which has weight of 9lb.

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Chapter 13.3, Problem 13.147P

Chapter 13.3, Problem 13.149P

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Find the impulsive force F Δ t and the energy absorbed ( Δ T ) by the rivet which has infinite mass.

Solution Summary: The author shows the free body momentum diagram of the hammer head and anvil as Figure (1).

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Find the impulsive force FΔt and the energy absorbed (ΔT) by the rivet which has infinite mass.

Find the impulsive force (FΔt) and the energy absorbed (ΔT) by the rivet which has weight of 9lb.

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