The surfer in the photo is catching a wave. Suppose she starts at the top of the wave with a speed of 1.35 m/s and moves down the wave until her speed reaches 11.6 m/s. The drop in her vertical height is 1.18 m. If her mass is 68.7 kg, how much work is done by the (non-conservative) force of the wave?
To determine the work done by the non-conservative force of the wave, we can use the work-energy principle. The work done by a force can be calculated using the formula:
Work = change in kinetic energy + change in potential energy
In this case, the surfer's initial kinetic energy is given by:
K_initial = (1/2) * m * v_initial^2
Where:
m = mass of the surfer = 68.7 kg
v_initial = initial speed of the surfer = 1.35 m/s
And the final kinetic energy is given by:
K_final = (1/2) * m * v_final^2
Where:
v_final = final speed of the surfer = 11.6 m/s
The change in potential energy is equal to the work done by the non-conservative force of the wave, which is what we want to find.
The potential energy can be calculated using the formula:
Potential energy = m * g * h
Where:
g = acceleration due to gravity = 9.8 m/s^2
h = drop in vertical height = 1.18 m
Substituting the given values, we have:
Potential energy = 68.7 kg * 9.8 m/s^2 * 1.18 m
Now, let's calculate the initial and final kinetic energies:
K_initial = (1/2) * 68.7 kg * (1.35 m/s)^2
K_final = (1/2) * 68.7 kg * (11.6 m/s)^2
The work done by the non-conservative force of the wave is then given by:
Work = K_final - K_initial + Potential energy
Substituting the values in the equation, we can find the solution.