A 1500 kg car moving at 10 m/s is stopped by the action of its brakes. The work done by the car's brakes is ____ Joules.
To find the work done by the car's brakes, we need to use the work-energy principle.
The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. In this case, the initial kinetic energy of the car is given by its mass (m) and velocity (v) using the formula:
Kinetic energy (KE) = 0.5 * m * v^2.
Given that the mass (m) of the car is 1500 kg and the velocity (v) is 10 m/s, we can calculate the initial kinetic energy:
KE_initial = 0.5 * 1500 kg * (10 m/s)^2
= 0.5 * 1500 kg * 100 m^2/s^2
= 75,000 J.
Since the car is being stopped by the brakes, its final velocity (v_final) is 0 m/s. Therefore, the final kinetic energy (KE_final) is also zero, as velocity is squared in the kinetic energy formula.
According to the work-energy principle, the work done by the car's brakes is equal to the change in kinetic energy:
Work done = KE_final - KE_initial
= 0 J - 75,000 J
= -75,000 J.
We get a negative value for work done because the brakes are opposing the motion of the car. Therefore, the work done by the car's brakes is -75,000 Joules.