A ball of mass 1000g moving with 7m/s impinges another ball of twice its own mass
and moving with 1/6th of its own velocity and moves in the opposite direction. If the coefficient of restitution is 0.75, calculate the velocities of the two balls after impact.
Pl help me
Take a look at this example. It is very similar to yours.
http://www.a-levelmathstutor.com/m-momimp-coeffrest.php
To solve this problem, we can use the law of conservation of linear momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
First, let's assign variables to the velocities of the two balls before the collision. Let's call the velocity of the 1000g ball "v1" and the velocity of the other ball "v2". Given that the 1000g ball has a velocity of 7m/s and the other ball has 1/6th of its own velocity, we can write the following equations:
v1 = 7 m/s
v2 = (1/6) * v1
Next, let's calculate the total momentum before the collision. Since momentum is mass times velocity, the momentum of the 1000g ball (m1) is given by:
momentum1 = mass1 * velocity1 = (1000g) * (7m/s) = 7000 g*m/s
Similarly, the momentum of the other ball (m2) is given by:
momentum2 = mass2 * velocity2 = (2000g) * [(1/6) * v1] = 2 * 1000g * (1/6) * v1 = (1000g) * (1/3) * v1 = (1/3) * momentum1
Now, let's apply the law of conservation of momentum. According to this law, the total momentum before the collision (momentum1 + momentum2) is equal to the total momentum after the collision.
momentum1 + momentum2 = momentum1' + momentum2'
Where momentum1' and momentum2' are the momenta of the balls after the collision.
Using the given coefficient of restitution (e = 0.75), we can write another equation:
e = (velocity2' - velocity1') / (velocity1 - velocity2)
Substituting the values we know:
0.75 = (v2' - v1') / (v1 - v2)
Now, let's solve these equations to find the velocities after the collision:
momentum1' + momentum2' = momentum1 + momentum2
v1' + v2' = 7m/s (since momentum1 = momentum1 and momentum2 = momentum2)
Also, we can substitute v1 and v2 in the second equation:
v1' + (1/6) * v1' = 7m/s
Combining the terms:
(7/6) * v1' = 7m/s
Simplifying:
v1' = (6/7) * 7m/s = 6m/s
From this, we can calculate v2':
v2' = 7m/s - v1' = 7m/s - 6m/s = 1m/s
Therefore, the velocity of the 1000g ball after the collision is 6m/s, and the velocity of the other ball is 1m/s.