Question

A 25.0 kg bumper car moving to the right at 5.00 m/s overtakes and col-
lides clastically with a 35.0 kg bumper car moving to the right. After the
collision, the 25.0 kg bumper car slows to 1.50 m/s to the right, and the
35.0 kg car moves at 4.50 m/s to the right.
a. Find the velocity of the 35 kg bumper car before the collision.
.b. Verify your answer by calculating the total kinetic energy before and
after the collision.​

Answer 1

Explanation:

This problem bothers elastic collision.

Given data

Mass m1= 25kg

Initial velocity u1= 5m/s

Final velocity v1= 1.5m/s

Mass m2= 35kg

Initial velocity u2=?

Final velocity v2 = 4.5m/s

A. To find the initial velocity of the 35kg car, let us Apply the principle of conservation of energy

m1u1+m2u2= m1v1+m2v2

25*5+ 35*u2= 25*1.5+ 35*4.5

125+35u2= 37.5+157.5

125+35u2=195

35u2= 195-125

35u2= 70

u2= 2m/s

The initial velocity is 2m/s

B. Totally not kinetic energy before impact

KE= 1/2m1u1²+ 1/2m2u2²

KE= (25*5²)/2+ (35*2²)/2

KE= 625/2 +140/2

KE= 312.5+70

KE= 382.5J

Total kinetic energy after impact

KE=1/2m1v1²+ 1/2m2v2²

KE= (25*1.5²)/2 +(35*4.5²)/2

KE= 56.25/2 +708.75/2

KE=28.125 +354.375

KE= 382.5J

We can see that energy is conserved

Kinetic energy before and after impact remains unchanged