A 0.20-kg softball is traveling at a velocity of 20 m/s to the east relative to

Question

A 0.20-kg softball is traveling at a velocity of 20 m/s to the east relative to Earth. It collides head-on with a 0.40-kg rubber ball traveling at a velocity of 10 m/s to the west. The system's kinetic energy, as measured from the Earth reference frame, decreases by 19 % because of the collision. Call the east the +x direction.

a) What is the x-component of the final velocity of the softball?

b) What is the x-component of the final velocity of the rubber ball?

c) What change in internal energy has occurred?

d) An observer watches this collision from a reference frame moving at a velocity of

15 m/s to the east relative to the Earth reference frame. What change in kinetic energy does this observer measure?

e) An observer watches this collision from a reference frame moving at a velocity of

15 m/s to the east relative to the Earth reference frame. What change in internal energy does this observer measure?

f) What change in kinetic energy would be measured by an observer in a reference frame traveling at

20 m/s east relative to the Earth reference frame?

g) What change in internal energy would be measured by an observer in a reference frame traveling at

20 m/s east relative to the Earth reference frame?

Explanation / Answer

let the final velocity of the softball be x and that of rubber ball be y.so,

applying law of conservation of momentum,

0.2*20 - 0.4*10 = 0.2*x + 0.4*y

also,

the final energy is 0.81 times the initial energy.

so, apply energy equation,

0.5*0.2*x^2 + 0.5*0.4*y^2 = 0.81*(0.5*0.2*20^2 + 0.5*0.4*10^2)

solving the aboe two equations, we get

x = 18 m/s (towards west)

y = 9 m/s(towards east)

a)18m/s towards west

b)9m/s towards right

c)change in internal energy = -0.19*(0.5*0.2*20^2 + 0.5*0.4*10^2)

=-11.4 J

d)inital energy with respect to the observer = 0.5*0.2*5^2 + 0.5*0.4*25^2 (considering relative velocity)

=127.5 J

final energy = 0.5*0.2*(15+18)^2 + 0.5*0.4*(6)^2

=116.1 J

change = 116.1 - 127.5

=-11.4 J

This could have been directly said as energy is a scalar quantity.

the answer is same for e,f,g ie.e -11.4 J (since energy is conserved always)

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