A tow truck attaches a cable to a car stuck in a muddy ditch. The 1250 kg car is pulled up an
embankment to a height of 1.8 m at a constant speed. The cable exerts a force of 5500 N over a
distance of 12.6 m to pull the car out of the ditch.
a) What is the amount of useful energy produced?
b) What amount of energy is used to pull the car from the ditch?
c) Calculate the percent efficiency.
To solve this problem, we need to use the formulas for work and gravitational potential energy. The work done by the cable is equal to the force applied multiplied by the distance over which it is applied:
Work = Force * Distance
a) The amount of useful energy produced is equal to the work done by the cable. Therefore, we can calculate it as:
Useful energy produced = Work = Force * Distance
Useful energy produced = 5500 N * 12.6 m
Useful energy produced = 69300 J
b) The amount of energy used to pull the car from the ditch is equal to the change in gravitational potential energy. Since the car is lifted to a height of 1.8 m, we can calculate it using the formula:
Change in gravitational potential energy = mass * gravity * height
change in gravitational potential energy = 1250 kg * 9.8 m/s^2 * 1.8 m
change in gravitational potential energy = 22050 J
c) The efficiency of the process is given by the ratio of the useful energy produced to the total energy used:
Efficiency = (Useful energy produced / Total energy used) * 100
Efficiency = (69300 J / (69300 J + 22050 J)) * 100
Efficiency = 75.84%
Therefore, the percent efficiency of pulling the car out of the ditch is approximately 75.84%.