when an object that is moving slows down, which action must be occurring? unbalanced forces unbalanced forces frictional force f
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Answer:
The acceleration is
Explanation:
From the question we are told that
The length of the stick is
The mass of the stick is
The angular displacement is
Generally the torque of this uniform stick after this displacement is mathematically represented as
Generally the moment of inertia of the uniform stick is mathematically represented as
=>
=>
Generally the angular acceleration is mathematically represented as
=>
=>
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.