A ball of mass 0.70 kg moving with speed of 1.0 m/s hits a wall and bounces back with the same speed in the opposite direction. What is the change in the ball's kinetic energy?
The speed doesn't change. What does that tell you?
If you don't know, review the definition of kinetic energy:
(1/2) M V^2
Even if the velocity changes sign, V^2 does not change sign.
The mass M doesn't change, either.
To find the change in the ball's kinetic energy, we first need to determine its initial and final kinetic energy.
The kinetic energy of an object is given by the formula:
Kinetic Energy = (1/2) * mass * velocity^2
Given:
Mass of the ball (m) = 0.70 kg
Initial velocity (u) = 1.0 m/s
Final velocity (v) = -1.0 m/s (opposite direction after bouncing back)
We can use the formula to calculate the initial and final kinetic energy:
Initial kinetic energy = (1/2) * m * u^2
Final kinetic energy = (1/2) * m * v^2
Substituting the given values into the formulas:
Initial kinetic energy = (1/2) * 0.70 kg * (1.0 m/s)^2
Final kinetic energy = (1/2) * 0.70 kg * (-1.0 m/s)^2
Calculating:
Initial kinetic energy = (1/2) * 0.70 kg * 1.0 m^2/s^2 = 0.35 Joules
Final kinetic energy = (1/2) * 0.70 kg * 1.0 m^2/s^2 = 0.35 Joules
The change in kinetic energy is given by the difference between the final and initial kinetic energies:
Change in kinetic energy = Final kinetic energy - Initial kinetic energy
Change in kinetic energy = 0.35 Joules - 0.35 Joules = 0 Joules
Therefore, the change in the ball's kinetic energy is 0 Joules.