an object of mass 10 kg is moving with a velocity of 10 metre per second and another object of mass 20 kg is moving with a velocity of 5 metre per second then the ratio of their momentum is
Answers
I'll assume this collision is direct rather than at an angle.
We will use the law of conservation of momentum. Since the collision is direct (assumed) there is only one direction of motion to consider using:
m1u1+m2u2=m1v1+m2v2
Where m1,2 are the masses of the two bodies, u1,2 are the initial velocities and v1,2 are the final velocities.
Filling in what we know
10(5)+0.001(0)=10v1+0.001v2
10v1+0.001v2=50
Now since the collision is perfectly elastic, the coefficient of restitution (e) is 1.
i.e.
−v1−v2u1−u2=1
−v1−v25−0=1
v1−v2=−5
Now we have two equations for v1 and v2
10v1+0.001v2=50
v1−v2=−5
From 2. we can get
v1=v2−5
Substituting back in to 1.
10(v2−5)+0.001v2=50
10v2−50+0.001v2=50
10.001v2=100
v2=10010.001=9.999ms−1
This is the required velocity.
We could then continue using 1. above to find that the first body continues to move in the same direction at 4.999ms−1 .
Thank you