A softball of mass 0.220 kg that is moving with a speed of 5.5 m/s (in the positive direction) collides head-on and elastically with another ball initially at rest. Afterward it is found that the incoming ball has bounced backward with a speed of 3.9 m/s. (a) Calculate the velocity of the target ball after the collision.
m/s
(b) Calculate the mass of the target ball.
kg
You will need two equations to solve for the two unknowns: target ball final velocity and mass.
The kinetic energy and momentum conservation equations, applied together, will let you solve for both.
Pleass show your work for further help.
1.21 kg times 5. m/s
To solve this problem, we can use the principles of conservation of momentum and conservation of kinetic energy.
(a) To calculate the velocity of the target ball after the collision, we need to calculate the velocity of the incoming ball after the collision first. According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity. Let's denote the velocity of the incoming ball after the collision as v1.
The momentum before the collision is computed as:
Initial momentum = mass of incoming ball * initial velocity of incoming ball = (0.220 kg) * (5.5 m/s)
The momentum after the collision is:
Final momentum = mass of incoming ball * velocity of incoming ball after the collision = (0.220 kg) * (-3.9 m/s)
Since momentum is conserved, we can set the initial momentum equal to the final momentum:
(0.220 kg) * (5.5 m/s) = (0.220 kg) * (-3.9 m/s)
By solving this equation, we can find the velocity of the incoming ball after the collision (v1).
(b) To calculate the mass of the target ball, we use the concept of conservation of kinetic energy. Since the collision is elastic, the total kinetic energy before the collision is equal to the total kinetic energy after the collision.
The kinetic energy of an object is given by (1/2) * mass * velocity^2. Let's denote the mass of the target ball as m2.
The initial kinetic energy before the collision is computed as:
Initial kinetic energy = (1/2) * mass of incoming ball * (initial velocity of incoming ball)^2 = (1/2) * (0.220 kg) * (5.5 m/s)^2
The final kinetic energy after the collision is equal to:
Final kinetic energy = (1/2) * mass of incoming ball * (velocity of incoming ball after the collision)^2 = (1/2) * (0.220 kg) * (-3.9 m/s)^2
Since kinetic energy is conserved, we can set the initial kinetic energy equal to the final kinetic energy:
(1/2) * (0.220 kg) * (5.5 m/s)^2 = (1/2) * (0.220 kg) * (-3.9 m/s)^2
By solving this equation, we can find the mass of the target ball (m2).
Now, let's go ahead and calculate the values of v1 (velocity of the incoming ball after collision) and m2 (mass of the target ball).