Elastic Collisions Practice Problems

In an experiment, a block of mass 2m is released from rest down the 4.2 m high curve, as shown. The block collides with a second block of mass 3m at the bottom of the curve. Assuming a perfectly elastic collision, determine the rebound height of the 2m block.

Two cars collide with each other. Car A has a mass of 1000 kg and is moving towards car B with a velocity of 20 m/s. Car B has a mass of 800 kg and is at rest. What is the velocity of each car immediately after they collide?

We assume this is a one-dimensional collision that obeys the conservation laws of momentum and
mechanical energy.

Two marbles collide head-on in an elastic collision. Marble A has a mass of 14 g and is initially moving to the right at 2.5 m/s, while Marble B has a mass of 12 g and is initially moving to the left at 3.2 m/s. Assume that motion to the right is considered positive, and motion to the left is considered negative. What will be the final speed and direction of each marble after the collision, assuming that the collision is perfectly elastic?

An alpha particle moves at a speed of 4.50 × 10 ⁶ m/s due north. The alpha particle collides elastically with a neon atom initially at rest. Taking the neon atom to be 5 times the mass of the alpha particle, determine the velocity (magnitude and direction) of the particles after the collision. Take the initial direction of the alpha particle as positive.

The image below shows the momenta of toys A and B before the collision, as well as the momentum of toy B after the collision. The toys separate after the collision. Determine the momentum of toy A after the collision, giving the result in unit vectors.

A 3.5 kg sphere moving at 3.2 m/s collides with a second sphere of equal mass initially at rest. The direction of the first sphere changes by 20 degrees, and its new speed is 2.5 m/s. Express the lost mechanical energy as a percentage of the system's mechanical energy before the collision.

Two identical marbles on a frictionless surface are initially at rest. They are then struck by a third identical marble moving horizontally at 1.5 m/s as shown in the figure below. After the collision, both of the first two marbles move at an angle of 45° to the initial path of the third marble. Assuming the collision is perfectly elastic, find the speeds of all three marbles post-collision.

A large underwater vehicle is tasked with stabilizing an ocean buoy by applying a gentle, elastic collision. The vehicle, which has a mass 30 times that of the buoy, approaches at a velocity of 5.0 m/s. The buoy is initially at rest, and the collision is planned to avoid any rotational effects on the buoy. Following the collision, the buoy is redirected at a 30° angle from the vehicle's initial direction. Calculate the post-collision speed of the buoy.

A spacecraft (mass = $720 \mathrm{~kg}$ ) traveling at $11.2\mathrm{\frac{km}{s}}$ in the + 𝑦 direction approaches Jupiter, which moves at $13.1\mathrm{\frac{km}{s}}$ in the - 𝑦 direction and has a mass of $1.90 \times 10^{27} \mathrm{~kg}$. During a gravity slingshot, the spacecraft curves around Jupiter, depicted by a dashed trajectory. Assuming only gravitational forces act and Jupiter's motion remains unaffected by the spacecraft, find the spacecraft's final speed after escaping Jupiter's gravity.

Two hockey pucks slide on a frictionless ice surface towards each other. The first puck, with a mass of 0.15 kg, moves to the right at a speed of 5.0 m/s, while the second puck, having a mass of 0.20 kg, moves to the left at 3.0 m/s. Assuming the collision between the pucks is perfectly elastic, calculate the final velocities of both pucks after the collision. Consider motion to the right to be in the positive direction.