Question

15. A 5.0 g coin sliding to the right at 25.0 cm/s makes an elastic head-on collision with a 15.0 g coin that is initially at rest. After the collision, the 5.0 g coin moves to the left at 12.5 cm/s. Find the final velocity of the other coin. (12.5 cm/s, Right)​

Answer 1

The 15.0 g coin moves to the right at 12.5 cm/s after an elastic collision with a 5.0 g coin, as determined by the conservation of momentum and kinetic energy.

The student's question involves an elastic collision between two coins of different masses, where one coin is initially at rest and the other is moving. After an elastic collision, the conservation of momentum and the conservation of kinetic energy are both applicable. Given that a 5.0 g coin slides to the right at 25.0 cm/s and collides with a 15.0 g coin at rest, the post-collision velocity of the 5.0 g coin is 12.5 cm/s to the left.

To find the final velocity of the 15.0 g coin, we use the conservation of momentum. The initial momentum of the system is (5.0 g)(25.0 cm/s) = 125 g·cm/s. After the collision, the 5.0 g coin's momentum is -(5.0 g)(12.5 cm/s) = -62.5 g·cm/s (negative because it's to the left). Therefore, the momentum of the 15.0 g coin must be 125 g·cm/s - (-62.5 g·cm/s) = 187.5 g·cm/s. To find the velocity, we divide the momentum by the mass, v = p/m, which gives us v = 187.5 g·cm/s / 15.0 g = 12.5 cm/s. Hence, the 15.0 g coin moves to the right at 12.5 cm/s.

Answer 2

Answer: Finally, we can use this value to find the final velocity of the 15.0 g coin. Since velocity is defined as the change in position over time, and the 15.0 g coin is initially at rest, its final velocity must be equal to its final momentum divided by its mass. Therefore, the final velocity of the 15.0 g coin is 187.5 g cm/s / 15.0 g = 12.5 cm/s. Since the 5.0 g coin is moving to the right and the 15.0 g coin is moving

Explanation: To solve this problem, we can use the conservation of momentum. Momentum is a measure of an object's motion and is defined as the product of its mass and velocity. In an elastic collision, momentum is conserved, meaning that the total momentum of the system before the collision is equal to the total momentum after the collision.

We can use this principle to find the final velocity of the 15.0 g coin. First, we need to calculate the initial momentum of the system. The 5.0 g coin has an initial momentum of 5.0 g * 25.0 cm/s = 125 g cm/s. Since the 15.0 g coin is initially at rest, its initial momentum is 0 g cm/s. The total initial momentum of the system is therefore 125 g cm/s.

After the collision, the 5.0 g coin moves to the left at 12.5 cm/s, so its final momentum is 5.0 g * (-12.5 cm/s) = -62.5 g cm/s. Since momentum is conserved, the final momentum of the system must be equal to the initial momentum of the system, so the final momentum of the 15.0 g coin must be 125 g cm/s - (-62.5 g cm/s) = 187.5 g cm/s.

Finally, we can use this value to find the final velocity of the 15.0 g coin. Since velocity is defined as the change in position over time, and the 15.0 g coin is initially at rest, its final velocity must be equal to its final momentum divided by its mass. Therefore, the final velocity of the 15.0 g coin is 187.5 g cm/s / 15.0 g = 12.5 cm/s. Since the 5.0 g coin is moving to the right and the 15.0 g coin is moving