Question

jonathan is riding a bicycle and encounters a hill of height 7.70 m. at the base of the hill, he is traveling at 7.00 m/s. when he reaches the top of the hill, he is traveling at 1.10 m/s. jonathan and his bicycle together have a mass of 82.0 kg. ignore friction in the bicycle mechanism and between the bicycle tires and the road. what is the total external work done on the system of jonathan and the bicycle between the time he starts up the hill and the time he reaches the top?

Answer 1

To find the total external work done on the system of Jonathan and the bicycle, we can use the work-energy theorem. We can calculate the initial and final kinetic energies using the given speeds and mass. Then, subtract the initial kinetic energy from the final kinetic energy to find the total external work done on the system.

Step-by-step explanation:

To find the total external work done on the system of Jonathan and the bicycle, we can use the work-energy theorem. The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. We can calculate the initial and final kinetic energies using the equations:

Kinetic Energy (initial) = 0.5 * mass * (speed)^2

Kinetic Energy (final) = 0.5 * mass * (speed)^2

The total external work done on the system is then the difference between the final and initial kinetic energies:

Total External Work = Kinetic Energy (final) - Kinetic Energy (initial)

Plugging in the given values, we have:

Initial Speed (v1) = 7.00 m/s

Final Speed (v2) = 1.10 m/s

Mass (m) = 82.0 kg

Using the equations, we can calculate the initial and final kinetic energies. Then, subtract the initial kinetic energy from the final kinetic energy to find the total external work done on the system.