A 0.280-kg ball makes an elastic head-on collision with a second ball initially at rest. The second ball moves off with one-fourth the original speed of the first ball. The mass of the second ball is

This problem can be solved using the principles of conservation of momentum and kinetic energy.

Step 1: Conservation of Momentum The total momentum before the collision is equal to the total momentum after the collision.

Let's denote: m1 = mass of the first ball = 0.280 kg u1 = initial velocity of the first ball v1 = final velocity of the first ball m2 = mass of the second ball (which we are trying to find) u2 = initial velocity of the second ball = 0 (since it's initially at rest) v2 = final velocity of the second ball = u1/4 (since it moves off with one-fourth the original speed of the first ball)

According to the conservation of momentum: m1u1 + m2u2 = m1v1 + m2v2

Substituting the known values: 0.280u1 + 0 = 0.280v1 + m2*(u1/4)

Step 2: Conservation of Kinetic Energy The total kinetic energy before the collision is equal to the total kinetic energy after the collision.

1/2m1u1^2 + 1/2m2u2^2 = 1/2m1v1^2 + 1/2m2v2^2

Substituting the known values: 1/20.280u1^2 + 0 = 1/20.280v1^2 + 1/2m2(u1/4)^2

Step 3: Solve the Equations Now you have two equations with two unknowns (v1 and m2). You can solve these equations simultaneously to find the values of v1 and m2.

Note: The problem does not provide the initial velocity of the first ball (u1), so we cannot calculate the exact values of v1 and m2. However, if u1 is given, you can follow the above steps to find the mass of the second ball.