(a)
The spring constant when ball is modelled as a spring.
(a)
Answer to Problem 57AP
The spring constant when ball is modelled as a spring is
Explanation of Solution
As steel ball is modelled as a spring this shows elastic behavior of the ball, so to calculate spring constant Hooke’s law is used.
Write the expression for force applied to the ball.
Here,
Rearrange above equation for
Conclusion:
Substitute
Thus, the spring constant when ball is modelled as a spring is
(b)
The interaction of the ball during the collision.
(b)
Answer to Problem 57AP
The interaction of the ball during the collision is for a nonzero time interval.
Explanation of Solution
The interaction of the ball during the collision is for a time interval because if the interaction of the balls were for instant and not for some time then the force exerted by each ball on the other could be infinite and that is not possible.
Therefore, the interaction is for some time interval.
Conclusion:
Thus, the interaction of the ball during the collision is for a nonzero time interval
(c)
The kinetic energy of each of the balls before they collide .
(c)
Answer to Problem 57AP
The kinetic energy of each of the balls before they collide is
Explanation of Solution
The Kinetic energy for both the balls remains same as they have equal mass and they are moving with the same speed.
Consider iron as the main constituent in the density of steel to calculate mass of the balls.
Write the expression for mass in terms of density.
Here,
Write the expression for volume of sphere.
Here,
Substitute
Write the expression for Kinetic energy.
Here,
Write the expression for radius.
Here,
Substitute
Conclusion:
Substitute
Substitute
Thus, the kinetic energy of each of the balls before they collide is
(d)
The maximum amount of compression each ball undergoes when the balls collide.
(d)
Answer to Problem 57AP
The maximum amount of compression each ball undergoes when the balls collide is
Explanation of Solution
The maximum amount of elastic potential energy each ball has when the balls collide is equal to the kinetic energy they have before collision.
Write the expression for elastic potential energy.
Here,
Write the expression for conservation of energy for this system.
Substitute
Rearrange equation (VI) for
Conclusion:
Substitute
Thus, the maximum amount of compression each ball undergoes when the balls collide is
(e)
The time interval for which the balls are in contact.
(e)
Answer to Problem 57AP
The time interval for which the balls are in contact is nearly
Explanation of Solution
The balls are in contact for a very small time and distance covered by them is the maximum amount of compression the ball undergoes when it collides with the average speed.
Write the expression for average speed of the ball.
Here,
Write the expression for time.
Here,
Conclusion:
Substitute
Substitute
The order of magnitude estimate for time interval is
Thus, the time interval for which the balls are in contact is nearly
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Chapter 7 Solutions
Physics: for Science.. With Modern. -Update (Looseleaf)
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