Which quantity is a scalar quantity?
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Refer to the diagram shown below.
Before collision, the momentum of the two masses is
P₁ = Mv + (10M)*0 = Mv
After the collision, assume that the lighter ball rebounds off the heavier ball with a coefficient of restitution of r, so that v₂ = rv.
If r = 1, the rebound is elastic and v₂ = -v.
If r < 1, the rebound velocity is v₂ = -rv.
If r= 0, the lighter ball sticks to the heavier ball.
The momentum after collision is
P₂ = -Mv₂ + 10Mv₁
Because momentum is conserved, P₁ = P₂. That is,
10Mv₁ - M(rv) = Mv
v₁ = v(1+r)/10 for r>0.
When r=1 (elastic rebound)
v₁ = v/5.
The heavier ball moves right at 20% of the velocity of the lighter ball,
and the lighter ball rebounds with its velocity in the opposite direction.
When 0 < r < 1,
v₁ = (1+r)/10.
The heavier ball travels with greater than 20% of the velocity of the lighter ball, and the lighter ball rebounds with a velocity less than its initial velocity.
When r=0, the balls will stick together and
(10M + M)v₁ = Mv
v₁ = v/11.
The stuck balls move together at 1/11 of the initial velocity of the lighter ball.
Before collision, the momentum of the two masses is
P₁ = Mv + (10M)*0 = Mv
After the collision, assume that the lighter ball rebounds off the heavier ball with a coefficient of restitution of r, so that v₂ = rv.
If r = 1, the rebound is elastic and v₂ = -v.
If r < 1, the rebound velocity is v₂ = -rv.
If r= 0, the lighter ball sticks to the heavier ball.
The momentum after collision is
P₂ = -Mv₂ + 10Mv₁
Because momentum is conserved, P₁ = P₂. That is,
10Mv₁ - M(rv) = Mv
v₁ = v(1+r)/10 for r>0.
When r=1 (elastic rebound)
v₁ = v/5.
The heavier ball moves right at 20% of the velocity of the lighter ball,
and the lighter ball rebounds with its velocity in the opposite direction.
When 0 < r < 1,
v₁ = (1+r)/10.
The heavier ball travels with greater than 20% of the velocity of the lighter ball, and the lighter ball rebounds with a velocity less than its initial velocity.
When r=0, the balls will stick together and
(10M + M)v₁ = Mv
v₁ = v/11.
The stuck balls move together at 1/11 of the initial velocity of the lighter ball.