(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 .

12th Edition

ISBN: 9781260663778

Author: BEER

Publisher: MCG

See similar textbooks

Videos

Question

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.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.3, Problem 13.147P

Chapter 13.3, Problem 13.149P

Students have asked these similar questions

A block with a mass of m is dropped from a certain height. An undeformed spring with a spring constant of 450 N/m is placed directly below it. The distance between the top of the spring and the block is 3 m. Determine the magnitude of velocity of the block just before it hits the spring (use principles of work and energy) and prove using kinematic equations Determine the deformation of the spring as the block reaches its lowest point. (use principles of work and energy) Determine the magnitude of the velocity of the block as the spring returns to its original length. use (principles of work and energy) hello please help thank youuuu very very urgent

A piston of mass m and cross-sectional area A is in equilibrium under the pressure p at the center of a cylinder closed at both ends. Assuming that the piston is moved to the left a distance a 2 and released, and knowing that the pressure on each side of the piston varies inversely with the volume, determine the velocity of the piston as it again reaches the center of the cylinder. Neglect friction between the piston and the cylinder and express your answer in terms of m, a, P and A.

Prior to takeoff, the pilot of a 3000-kg twin-engine airplane tests the reversible-pitch propellers by increasing the reverse thrust with the brakes at point B locked. Knowing that point G is the center of gravity of the airplane, determine the velocity of the air in the two 2.2-m-diameter slipstreams when the nose wheel A begins to lift off the ground. Assume P = 1.21 kg/m3 and neglect the approach velocity of the air.

Chapter 13 Solutions

VECTOR MECH. FOR EGR: STATS & DYNAM (LL

Ch. 13.1 - Block A is traveling with a speed v0 on a smooth...Ch. 13.1 - A 400-kg satellite is placed in a circular orbit...Ch. 13.1 - A 0.5-lb stone is dropped down the bottomless pit...Ch. 13.1 - A baseball player hits a 5.1-oz baseball with an...Ch. 13.1 - A 500-kg communications satellite is in a circular...Ch. 13.1 - Prob. 13.5P Ch. 13.1 - In an ore-mixing operation, a bucket full of ore...Ch. 13.1 - Determine the maximum theoretical speed that may...Ch. 13.1 - A 2000-kg automobile starts from rest at point A...Ch. 13.1 - An athlete is holding 30 lb of weights at a height...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

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).

Videos

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.

Want to see the full answer?

Chapter 13 Solutions