a.
To show: Final velocities are
a.
Explanation of Solution
Given:
An object of mass mA and velocity vA elastically striking an stationary object ( vB =0) mass mB
Formula used:
According to energy conservation,
Calculation:
By the law of conservation of energy
(1)
Now, applying law of conservation of linear momentum,
(2)
Divide equation (1) by (2),
(3)
Substituting the value of
Rearranging this equation
Substituting the value of
b.
To explain: The effect on the final velocities for the given condition.
Also, state an example.
b.
Answer to Problem 30P
Explanation of Solution
Given:
An object of mass mA and velocity vA elastically striking an stationary object ( vB =0) mass mB
Formula used:
According to energy conservation,
Calculation:
From part (a),
When mA is much smaller than mB , then mA can be neglected. Substituting the values in final velocities expression,
Now,
Example for such a case is a rubber ball thrown against a wall.
c.
To explain: The effect on the final velocities for the given condition along with an example.
c.
Answer to Problem 30P
Object A will move with the same velocity and object B will move double the initial velocity of object A.
Explanation of Solution
Given:
An object of mass mA and velocity vA elastically striking an stationary object ( vB =0) mass mB .
Formula used:
According to energy conservation,
Calculation:
From part (a),
When mA is much larger than mB , then it can be neglected. Substituting the values,
Now,
This means object A will move with the same velocity but in opposite direction while object B will move with double the initial velocity of an object A
Example for such a case is collision between a fast moving truck and a stationary drum.
d.
To explain: The effect on the final velocities for the given condition along with an example.
d.
Answer to Problem 30P
This means object A will come to rest and object B will move with the same velocity as the initial velocity of object A.
Explanation of Solution
Given:
An object of mass mA and velocity vA elastically striking an stationary object ( vB =0) mass mB .
Formula used:
According to energy conservation,
Calculation:
From part (a),
When mA is equal to mB , substituting the values,
Now,
This means object A will come to rest and object B will move with the same velocity as the initial velocity of object A.
Example: When a ball at a billiard table hits another ball, the first ball stops, and second ball moves with the speed of the first ball.
Chapter 7 Solutions
Physics: Principles with Applications
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