Explanation Calculation: Express the velocity of mass centre using conservation of momentum as follows: ( m A + m B ) v ¯ = m A v A + m B v B v ¯ = m A v A + m B v B m A + m B Express the velocities to the mass centre as follows: v ′ A = v A − v ¯ (1) Here, v ¯ is velocity of mass centre. Substitute m A v A + m B v B m A + m B for v ¯ in Equation (1). v ′ A = v A − m A v A + m B v B m A + m B = m B ( v A + v B ) m A + m B Express the velocities to the mass centre as follows: v ′ B = v B − v ¯ (2) Substitute m A v A + m B v B m A + m B for v ¯ in Equation (2). v ′ B = v B − m A v A + m B v B m A + m B = m A ( v A + v B ) m A + m B Express the energy ( E A ) using the relation as follows: E A = 1 2 m A v ′ A ⋅ v ′ A (3) Substitute m B ( v A + v B ) m A + m B for v ′ A in Equation (3). E A = 1 2 m A ( m B ( v A + v B ) m A + m B ) ⋅ ( m B ( v A + v B ) m A + m B ) = m A m B 2 ( v A + v B ) ( v A + v B ) 2 ( m A + m B ) 2 Express the energy ( E B ) using the relation as follows: E B = 1 2 m B v ′ B ⋅ v ′ B (4) Substitute m A ( v A + v B ) m A + m B for v ′ B in Equation (4). E B = 1 2 m B m A ( v A + v B ) m A + m B B ⋅ m A ( v A + v B ) m A + m B = m A 2 m B ( v A + v B ) ( v A + v B ) 2 ( m A + m B ) 2 Express the energy ( E A ) 0 , ( E B ) 0 test as follows: ( E A ) 0 = 1 2 m A v 0 2 ( E B ) 0 = 1 2 m B v 0 2 Write the expression for sever for automobile A as follows: S A = E A ( E A ) 0 (5) Here, E A is energy and ( E A ) 0 is energies from tests

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

See similar textbooks

Concept explainers

Thermal Properties of Materials

In mechanical engineering, the thermal property is represented as the physical quantity that is relevant to the application of heat. The thermal properties are evaluated by variations in any specific material due to low heat or high heat. The quantities …

Videos

Question

Chapter 14.2, Problem 14.36P

To determine

Verify the given described collision between two automobile is (mAmB)2 times more severe for the automobile B than for automobile A.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.2, Problem 14.35P

Chapter 14.2, Problem 14.37P

Students have asked these similar questions

4. A 750 kg hammer is used to drive a 2500 kg pile into some loosely packed sand. The hammer is released from a height of 2.5 m above the top of the pile and is seen to rebound to a maximum height of 0.15 m above the point of impact. Determine: (a) the velocity of the pile immediately after impact, (b) the coefficient of restitution, and (c) the average force exerted by the hammer on the pile if the impact takes place over 0.08 s. 2.5 m P Ans. vp, = -2.62 m/s, e = 0.62, Favg = 81.9 kN %3D

14.35 Two automobiles A and B, of mass mĄ and m³, respectively, are traveling in opposite directions when they collide head on. The impact is as- sumed perfectly plastic, and it is further assumed that the energy absorbed by each automobile is equal to its loss of kinetic energy with respect to a moving frame of reference attached to the mass center of the two-vehicle system. Denoting by EA and EB, respectively, the energy absorbed by auto- mobile A and by automobile B, (a) show that EA/EB = mB/mA, that is, the amount of energy absorbed by each vehicle is inversely proportional to its mass, (b) compute EA and EB, knowing that mA = 2400 kg and mg = 1350 kg and that the speeds of A and B are, respectively, 135 km/h and 90 km/h. VB B

Q.2 Cylinder A is dropped from 2.4 m onto cylinder B, which is resting on a spring of constant k=300 N/m. Assuming perfectly plastic impact between 0.5 kg cylinders A and B, determine: a. The maximum deflection of cylinder B after impact b. The loss of energy during impact. 2.4 m During impact, ignore gravity and spring forces B 2.5 kg

Chapter 14 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 14.1 - A 30-g bullet is fired with a horizontal velocity...Ch. 14.1 - Two identical 1350-kg automobiles A and B are at...Ch. 14.1 - Prob. 14.3P Ch. 14.1 - Prob. 14.4P Ch. 14.1 - Two swimmers A and B, of weight 190 lb and 125 lb,...Ch. 14.1 - A 180-lb man and a 120-lb woman stand side by side...Ch. 14.1 - A 40-Mg boxcar A is moving in a railroad...Ch. 14.1 - Two identical cars A and B are at rest on a...Ch. 14.1 - A 20-kg base satellite deploys three...Ch. 14.1 - For the satellite system of Prob. 14.9, assuming...

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.

Verify the given described collision between two automobile is ( m A m B ) 2 times more severe for the automobile B than for automobile A .

Solution Summary: The author explains that the collision between two automobiles is (m_A)2 times more severe for the automobile B than for automobile A.

Concept explainers

Videos

Verify the given described collision between two automobile is (mAmB)2 times more severe for the automobile B than for automobile A.

Want to see the full answer?

Chapter 14 Solutions