How to Calculate Work Done by Air Resistance in a Physics Problem

Question:

How can we find the work done by air resistance in a physics problem involving a motorcyclist attempting to leap across a canyon?

Answer:

The work done by air resistance on the motorcyclist can be found by calculating the difference in mechanical energy from the initial to the final state. After performing the calculations, the work by air resistance is found to be -7500 J, indicating that option C) -7500 J is correct.

To determine the work done by air resistance, we must first analyze the change in mechanical energy of the motorcyclist as he goes from the higher to the lower cliff. Mechanical energy consists of kinetic and potential energy; in this problem, both will change due to the motion and elevation change.

We can use the conservation of mechanical energy formula to calculate the initial and final mechanical energy, provided air resistance has done work on the system:

ME_i = KE_i + PE_i

ME_f = KE_f + PE_f

The work done by air resistance (W_air) is the difference between the initial and final mechanical energy:

W_air = ME_f - ME_i

Calculating the individual energies:

KE_i = (1/2) * m * v_i²

PE_i = m * g * h_i

KE_f = (1/2) * m * v_f²

PE_f = m * g * h_f

After solving the above equations and substituting the given values, the work done by air resistance will be calculated as -7500 J, indicating that air resistance has done negative work on the system (opposed the motion), taking away energy.