Explanation Given information: The three sphere A , B , C each having mass is m . Calculation: Consider x is a distance between A and C . Calculate the horizontal distance ( x ) as shown below. l 2 = x 2 + ( l 3 ) 2 x 2 = l 2 − l 2 9 x 2 = 9 l 2 − l 2 9 x = 8 3 l Calculate angle θ as shown below. l sin θ = l 3 sin θ = 1 3 θ = 19.47 ° l cos θ = 8 3 l cos θ = 8 3 Sketch the velocity system as shown in Figure 1. Refer to Figure 1. Write the velocity vectors as follows: v 0 = − v 0 j v A = v A ( cos θ i − sin θ j ) v B / A = u B ( − sin θ i − cos θ j ) Express the velocity at B as follows: ( v B ) 2 = ( v A ) 2 + ( v B / A ) 2 v B = v A 2 + v B / A 2 Express the velocity at C as follows: v C = v C j Apply the conservation of momentum as follows. m v 0 = m v A + m v B / A + m v C = 2 m v A + m v B / A + m v C (1) Divided by m in Equation (1). m v 0 m = 2 m v A + m v B / A + m v C m v 0 = 2 v A + v B / A + v C (2) Substitute − v 0 j for v 0 , v A ( cos θ i − sin θ j ) for v A , v C j for v C , and u B ( cos θ i − cos θ j ) for v B / A in Equation (2). − v 0 j = 2 v A ( cos θ i − sin θ j ) + u B ( − sin θ i − cos θ j ) + v C j = v A cos θ i − v A sin θ j − u B sin θ i − u B cos θ j + v C j Resolving the components of i, j coordinates as follows: 2 v A cos θ − u B sin θ = 0 (3) v 0 = 2 v A sin θ + u B cos θ − v C (4) Solve Equation (3) and (4) as follows: v A = 1 6 ( v 0 + v C ) u B = 0.94281 ( v 0 + v C ) Find the velocity of sphere C using conservation of energy as follows: 1 2 m v 0 2 = 1 2 m v A 2 + 1 2 m v B 2 + 1 2 m v C 2 = 1 2 m v A 2 + 1 2 m ( v A 2 + u B 2 ) + 1 2 m v C 2 (5) Divided by 1 2 m in Equation (5)

11th Edition

ISBN: 9781259633133

Author: BEER

Publisher: MCG

See similar textbooks

Concept explainers

Strain energy

The term strain indicates the variation in an object's length, area, and volume when the object is subjected to an external force. The external force may be of normal, shear, moment, torque, etc. The strain in an object depends on the types of external f…

Videos

Question

Chapter 14.2, Problem 14.43P

To determine

Find the velocity of each sphere after impact.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.2, Problem 14.42P

Chapter 14.2, Problem 14.44P

Students have asked these similar questions

please show a drawing/image and explain how to properly do the question. thanks

For the four-bar- linkage shown in the following figure. BC=68mm, CD=100mm, AD=120mm. Determine the range of AB to make it a crank-rocker mechanism. B D

all of those 4 fi 1)Draw kinematic diagram: 2)DOF: 3)type/name of mechanism 4)evolution:

Chapter 14 Solutions

VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS

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.

Find the velocity of each sphere after impact.

Solution Summary: The author calculates the velocity of spheres A, B, and C after impact.

Concept explainers

Videos

Find the velocity of each sphere after impact.

Want to see the full answer?

Chapter 14 Solutions