A 110g ball moving to the right at 4.5m/s catches up and collides with a 410g ba

ID: 1294654 • Letter: A

Question

A 110g ball moving to the right at 4.5m/s catches up and collides with a 410g ball that is moving to the right at 1.1m/s .

Part A. If the collision is perfectly elastic, what is the speed of the 110g ball after the collision?

Part B. If the collision is perfectly elastic, what is the direction of motion of the 110g ball after the collision? ( to the left or to the right) ?

Part C.If the collision is perfectly elastic, what is the speed of the 410g ball after the collision?

Part D. f the collision is perfectly elastic, what is the direction of motion of the 410g ball after the collision? ( to the left or to the right)?

for elastic collisions

according to conservation of linear momentum

m1*u1 + m2*u2 = m1*v1+m2*v2

m1*(u1-v1) = m2*(v2-u2)........(1)

according to conservation of energy

0.5*m1*u1^2 + 0.5*m2*u2^2 = 0.5*m1*v1^2 + 0.5*m2*v2^2

m1*(u1^2 - v1^2) = m2*(v2^2-u2^2).....(2)

from 1 &2

u1 + v1 = u2+v2

u1 - u2 = v2 - v1

v2 = u1 - u2 + v1........(3)

3 in 1

m1*(u1-v1) = m2*(u1 - u2 + v1 - u2)

v1 = u1*(m1-m2)/(m1+m2) + 2*m2*u2/(m1+m2)

v2 = u2*(m2-m1)/(m1+m2) + 2*m1*u1/(m1+m2)

m1 = 0.110 kg.....m2 = 0.410 kg

u1 = 4.5 m/s ...........u2 = +1.1 m/s

#a)

v1 = (((0.11-0.410)*4.5) + (2*0.41*1.1))/(0.11+0.41)

v1 = -0.8615 m/s

#b) left

#c)

v2 = (((0.41-0.110)*1.1) + (2*0.11*4.5))/(0.11+0.41)

v2= +2.538 m/s

#d)

right

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