A 2 kg object moving with a velocity of +5 m/s collides with a 4 kg object that is initially at rest. After the collision, the 2 kg object moves with a velocity of -1 m/s.
(a) Find the velocity of the 4 kg object after the collision.
(b) Find the energy lost in the collision.
c) What is the coefficient of restitution for this collision?
for a i got 3ml/s
1.33m/s
To solve this problem, we can use the principle of conservation of momentum and the equation for kinetic energy.
(a) To find the velocity of the 4 kg object after the collision, we can use the conservation of momentum equation:
Before collision: momentum1 = mass1 × velocity1 = (2 kg) × (5 m/s) = 10 kg·m/s
After collision: momentum2 = mass1 × velocity2 + mass2 × velocity3
= (2 kg) × (-1 m/s) + (4 kg) × velocity3
Using the principle of conservation of momentum, we can equate the two expressions:
10 kg·m/s = -2 kg·m/s + 4 kg × velocity3
Simplifying the equation:
12 kg·m/s = 4 kg × velocity3
Dividing both sides by 4 kg:
velocity3 = 3 m/s
Therefore, the velocity of the 4 kg object after the collision is +3 m/s.
(b) To find the energy lost in the collision, we need to calculate the initial and final kinetic energies:
Initial kinetic energy = 0.5 × mass1 × (velocity1)^2
= 0.5 × 2 kg × (5 m/s)^2
= 25 J
Final kinetic energy = 0.5 × mass1 × (velocity2)^2 + 0.5 × mass2 × (velocity3)^2
= 0.5 × 2 kg × (-1 m/s)^2 + 0.5 × 4 kg × (3 m/s)^2
= 1 J + 18 J
= 19 J
The energy lost in the collision is the difference between the initial and final kinetic energies:
Energy lost = Initial kinetic energy - Final kinetic energy
= 25 J - 19 J
= 6 J
Therefore, the energy lost in the collision is 6 Joules.
(c) The coefficient of restitution (e) is a measure of the relative velocity of separation to the relative velocity of approach of two colliding objects. It is given by the formula:
e = (velocity3 - velocity2) / (velocity1 - velocity2)
Substituting the values we found earlier:
e = (3 m/s - (-1 m/s)) / (5 m/s - (-1 m/s))
= 4 m/s / 6 m/s
= 2/3
Therefore, the coefficient of restitution for this collision is 2/3.