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.
To find the work done by the frictional forces, we need to calculate the change in mechanical energy of the woman as she skis down the hill.
The mechanical energy consists of potential energy (PE) and kinetic energy (KE).
1. First, let's calculate the potential energy (PE) at the top of the hill using the formula:
PE = m * g * h
Where:
m = mass of the woman = 75 kg
g = acceleration due to gravity = 9.8 m/s²
h = height of the hill = 50 m
PE = 75 kg * 9.8 m/s² * 50 m = 36,750 J
2. Next, let's calculate the kinetic energy (KE) at the bottom of the hill using the formula:
KE = 1/2 * m * v²
Where:
m = mass of the woman = 75 kg
v = velocity at the bottom of the hill = 25 m/s
KE = 1/2 * 75 kg * (25 m/s)² = 23,437.5 J
3. The work done by friction is equal to the change in mechanical energy:
Work = PE - KE
Work = 36,750 J - 23,437.5 J = 13,312.5 J
Therefore, the work done by the frictional forces is 13,312.5 Joules.