Question: A 2.0 kg sphere with a velocity of 6.0 m/s collides head-on and elastically with a stationary 10 kg sphere, What is thier velocities after collision.
Answer:
v = 6 m/s, v' = 0 m/s
Explanation:
From the question,
For Elastic collision,
mu+m'u' = mv+m'v'......................... Equation 1
Where m = mass of the first sphere, m' = mass of the second sphere, u = initial velocity of the first sphere, u' = initial velocity of the second sphere, v = final veolocity of the first sphere, v' = final velocity of the second sphere.
Also,
The relative velocity before collision = relative velocity after collision
u-u' = v-v'............................ Equation 2
Given: m = 2 kg, m' = 10 kg, u = 6 m/s, u' = 0 m/s
Substitute into equation 1 and 2
2(6)+10(0) = 2v+10v'
2v+10v' = 12.............. Equation 3
6-0 = v-v'
v-v' = 6 ................... Equation 4
Solve equation 3 and 4 simultaneously.
v = 6+v'............. Equation 5
Substitute equation 5 into equation 3
2(6+v')+10v' = 12
12+2v'+10v' = 12
12v' = 12-12
v' = 0/12
v' = 0 m/s.
Also substitute the value of v' into equation 5
v = 6+0
v = 6 m/s
