Concept explainers
A test machine that kicks soccer balls has a 5-lb simulated foot attached to the end of a 6-ft long pendulum arm of negligible mass. Knowing that the arm is released from the horizontal position and that the coefficient of restitution between the foot and the 1-lb ball is 0.8, determine the exit velocity of the ball (a) if the ball is stationary, (b) if the ball is struck when it is rolling toward the foot with a velocity of 10 ft/s.
Fig. P13.184
(a)
Find the exit velocity of the ball
Answer to Problem 13.184P
The exit velocity of the ball
Explanation of Solution
Given information:
The weight of the stimulated foot
The weight of the ball
The length of the pendulum arm (l) is
The coefficient of restitution between the foot (e) is 0.8.
The angle
The acceleration of gravity (g) is
Calculation:
Calculate the mass of the stimulated foot
Substitute
Calculate the mass of the ball
Substitute
Calculate the speed of the foot
Here,
Substitute 0 for
Substitute
Show the impulse momentum diagram for the ball and foot as Figure (1).
The expression for the velocity of the ball
The expression for the conservation of momentum of the ball in tangent t direction as follows:
Substitute
Substitute
The expression for the speed of the ball
The expression for the conservation of momentum of the system in x direction as follows:
Substitute
The expression for the velocity of foot
The expression for the velocity of foot
The expression for the velocity of ball
The expression for the coefficient of restitution for both ball and foot in normal direction as follows:
Substitute
Substitute
Solve the equations (2) and (3).
Calculate the magnitude of the exit velocity of the ball
Substitute
The velocity of the ball
Substitute 0 for
Calculate the direction of the velocity of the ball
Substitute
Substitute 0 for
Therefore, the exit velocity of the ball
(b)
Find the exit velocity of the ball
Answer to Problem 13.184P
The exit velocity of the ball
Explanation of Solution
Given information:
The weight of the stimulated foot
The weight of the ball
The length of the pendulum arm (l) is
The coefficient of restitution between the foot (e) is 0.8.
The angle
The velocity
Calculation:
Calculate the magnitude of the exit velocity of the ball
Substitute
Substitute
Calculate the direction of the velocity of the ball
Substitute
Substitute 0 for
Therefore, the exit velocity of the ball
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Chapter 13 Solutions
Connect 2 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics
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