A 2 kg object is moving with a velocity of 5 m/s. If it collides elastically with a stationary object of mass 3 kg, what will be the final velocity of the 2 kg object?
Practice Questions
1 question
Q1
A 2 kg object is moving with a velocity of 5 m/s. If it collides elastically with a stationary object of mass 3 kg, what will be the final velocity of the 2 kg object?
1 m/s
2 m/s
3 m/s
4 m/s
Using conservation of momentum and kinetic energy, the final velocity of the 2 kg object after an elastic collision is 1 m/s.
Questions & Step-by-step Solutions
1 item
Q
Q: A 2 kg object is moving with a velocity of 5 m/s. If it collides elastically with a stationary object of mass 3 kg, what will be the final velocity of the 2 kg object?
Solution: Using conservation of momentum and kinetic energy, the final velocity of the 2 kg object after an elastic collision is 1 m/s.
Steps: 9
Step 1: Identify the masses and initial velocities of both objects. The first object has a mass of 2 kg and an initial velocity of 5 m/s. The second object has a mass of 3 kg and is stationary, so its initial velocity is 0 m/s.
Step 2: Write down the conservation of momentum formula. The total momentum before the collision equals the total momentum after the collision.
Step 3: Calculate the initial momentum of both objects. For the 2 kg object: 2 kg * 5 m/s = 10 kg*m/s. For the 3 kg object: 3 kg * 0 m/s = 0 kg*m/s. Total initial momentum = 10 kg*m/s + 0 kg*m/s = 10 kg*m/s.
Step 4: Let the final velocity of the 2 kg object be v1 and the final velocity of the 3 kg object be v2. Write the momentum conservation equation: 10 kg*m/s = 2 kg * v1 + 3 kg * v2.
Step 5: Write down the conservation of kinetic energy formula. The total kinetic energy before the collision equals the total kinetic energy after the collision.
Step 6: Calculate the initial kinetic energy of both objects. For the 2 kg object: 0.5 * 2 kg * (5 m/s)^2 = 25 J. For the 3 kg object: 0.5 * 3 kg * (0 m/s)^2 = 0 J. Total initial kinetic energy = 25 J + 0 J = 25 J.
Step 7: Write the kinetic energy conservation equation: 25 J = 0.5 * 2 kg * (v1)^2 + 0.5 * 3 kg * (v2)^2.
Step 8: Now you have two equations: one from momentum and one from kinetic energy. Solve these equations simultaneously to find v1 and v2.
Step 9: After solving the equations, you will find that the final velocity of the 2 kg object (v1) is 1 m/s.
