Two identical steel balls, each of diameter 24.8 mm and moving in opposite direc

Question

Two identical steel balls, each of diameter 24.8 mm and moving in opposite directions at 2 m/s, run into each other head-on and bounce apart. Prior to the collision, one of the balls is squeezed in a vise precise measurements are made of the resulting amount of compression. The results show that Hooke's law is a fair model for the ball's elastic behavior. For one datum, a force of 25 kN exerted by each jaw of the vise results in a 0.4-mm reduction in the ball's diameter. The diameter returns to its original value when the force is removed. Modeling the ball as a spring, find its spring constant.

(a) Modeling the ball as a spring, find the spring constant.
=62500000 N/m

(b) Does the interaction of the balls during the collision last only for an instant or for a nonzero time interval?

instantnonzero time interval

(c) Compute an estimate for the kinetic energy of each of the balls before they collide. (Assume the density of steel is 7860 kg/m3.)
= J

(d) Compute an estimate for the maximum amount of compression each ball undergoes when they collide.
= mm

(e) Compute an order-of-magnitude estimate for the time interval for which the balls are in contact.
= s

I already answered a & b, I only need help with c, d, and e.

Explanation / Answer

part C: Kinetic energy of each ball = 0.5 mv^2

here from density D = mass/volume

mass = D V = 7860 * 4* 3.14 * 12.4 e-3 *12.4 e-3* 12.4 e-3/3

0.0627 kgs

so KE = 0.5 * 0.0627 * 2*2 = 0.125 J of each ball

-------------------------------------------------

part D:

apply 0.5 kx^2 = 0.5mv^2

x^2 = 0.0627 * 2*2)/(62500000)

x = 0.0633 m

----------------------------------------------

apply impulse J = Ft = m(v-u)

t = 0.0627 *(2-(-2)/25000

t = 10*10^-6 us

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