Awoman of 75kg skis down a 50m high hill , the frictional force is not negligible her speed at the bottom of the hill is only 25m\sec, What is the work done by the frictional forces.
PE=KE+W(fr)
W(fr)=PE-KE=mgh-mv²/2
To find the work done by the frictional forces, we need to calculate the change in kinetic energy of the woman as she skis down the hill.
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 frictional force does negative work on the woman, causing a decrease in her kinetic energy.
First, let's calculate the initial potential energy of the woman at the top of the hill. The potential energy is given by the formula:
Potential energy = mass × gravitational acceleration × height
In this case:
Mass (m) = 75 kg
Gravitational acceleration (g) = 9.8 m/s^2
Height (h) = 50 m
Potential energy at the top = 75 kg × 9.8 m/s^2 × 50 m = 36,750 Joules
Next, let's calculate the final kinetic energy of the woman at the bottom of the hill. The kinetic energy is given by the formula:
Kinetic energy = 0.5 × mass × velocity^2
In this case:
Mass (m) = 75 kg
Velocity (v) = 25 m/s
Kinetic energy at the bottom = 0.5 × 75 kg × (25 m/s)^2 = 23,437.5 Joules
To find the work done by the frictional forces, we need to calculate the change in kinetic energy:
Change in kinetic energy = Final kinetic energy - Initial kinetic energy
Change in kinetic energy = 23,437.5 Joules - 0 Joules = 23,437.5 Joules
Therefore, the work done by the frictional forces is -23,437.5 Joules. The negative sign indicates that the work done is against the motion, as the frictional force opposes the woman's motion down the hill.