A cart of mass M1 = 5.00 kg and initial speed = 3.00 m/s collides head on with a second cart of mass M2 = 3.00 kg at rest. Assuming that the collision is elastic, find the speed of M2 after the collision.
I have tried the answer 5.0 m/s however it says it is wrong. Please help!
To find the speed of M2 after the collision, we can use the principle of conservation of momentum. In an elastic collision, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity: momentum = mass × velocity.
Before the collision, the momentum of the first cart (M1) is given by M1 × v1 (mass × velocity), where v1 is the initial speed of M1.
According to the problem, M2 is at rest initially, so its momentum before the collision is zero.
After the collision, the first cart's momentum is given by M1 × v1' (mass × final velocity), and the second cart's momentum (M2) is given by M2 × v2' (mass × final velocity).
Since the collision is elastic, the total momentum before the collision is equal to the total momentum after the collision. So we have:
M1 × v1 = M1 × v1' + M2 × v2'
Plugging in the given values, we have:
5.00 kg × 3.00 m/s = 5.00 kg × v1' + 3.00 kg × v2'
Simplifying the equation:
15.00 kg·m/s = 5.00 kg × v1' + 3.00 kg × v2'
To solve for v2', we need another equation. In an elastic collision, the total kinetic energy before the collision is equal to the total kinetic energy after the collision. The kinetic energy of an object is given by the formula: (1/2) × mass × velocity^2.
Before the collision, the total kinetic energy is given by (1/2) × M1 × (v1)^2, since cart M1 is the only cart moving. After the collision, the total kinetic energy is given by (1/2) × M1 × (v1')^2 + (1/2) × M2 × (v2')^2.
Setting the initial kinetic energy equal to the final kinetic energy, we have:
(1/2) × M1 × (v1)^2 = (1/2) × M1 × (v1')^2 + (1/2) × M2 × (v2')^2
Plugging in the given values, we have:
(1/2) × 5.00 kg × (3.00 m/s)^2 = (1/2) × 5.00 kg × (v1')^2 + (1/2) × 3.00 kg × (v2')^2
Simplifying this equation:
(1/2) × 5.00 kg × 9.00 m^2/s^2 = (1/2) × 5.00 kg × (v1')^2 + (1/2) × 3.00 kg × (v2')^2
Now we have a system of two equations with two unknowns (v1' and v2'). Solving these equations simultaneously will give us the final velocities of both carts.
15.00 kg·m/s = 5.00 kg × v1' + 3.00 kg × v2'
22.50 kg·m^2/s^2 = 5.00 kg × (v1')^2 + 1.50 kg × (v2')^2
Solving this system of equations will yield the final speed of M2 after the collision.