Question

A 2.0-kg object is at rest on a perfectly frictionless surface when it is hit by a 3.0-kg object moving at \(8.0 \mathrm{m} / \mathrm{s}\) If the two objects are stuck together after the collision, what is the speed of the combination?

Short answer

Answer: The velocity of the combined objects after the collision is 4.8 m/s.

Step-by-step solution

Calculate the initial momentum of the system

To calculate the initial momentum of the system (before the collision), we need to consider the momentum of both objects. Since the stationary object is not moving, it doesn't contribute to the initial momentum. For the moving object: momentum_1 = mass_1 * velocity_1 where mass_1 = 3.0 kg (mass of the moving object) velocity_1 = 8.0 m/s (velocity of the moving object) momentum_1 = 3.0 kg * 8.0 m/s = 24 kg*m/s The initial momentum of the system is 24 kg*m/s.

Apply the conservation of linear momentum

According to the conservation of linear momentum, the initial momentum of the system should be equal to the final momentum of the system after the collision. Since both the objects are stuck together after the collision, we can treat them as one object with a total mass of (mass_1 + mass_2) and a common velocity (let's call it v_f): mass_2 = 2.0 kg (mass of stationary object) momentum_final = (mass_1 + mass_2) * v_f = 24 kg*m/s (from step 1)

Calculate the velocity of combined objects after collision

To find the velocity of the combined objects after the collision, we need to solve the equation obtained in step 2 for v_f: v_f = momentum_final / (mass_1 + mass_2) v_f = 24 kg*m/s / (3.0 kg + 2.0 kg) v_f = 24 kg*m/s / 5.0 kg v_f = 4.8 m/s The velocity of the combined objects after the collision is 4.8 m/s.