A 100hp motor raises a 2080lb elevator 200ft in 10s. How much energy is lost during 10s?
To calculate the energy lost during the 10-second period, you can first find the amount of work done by the motor to raise the elevator. Then, you can compare that to the efficiency of the motor to determine the amount of energy lost.
First, let's calculate the work done by the motor. Work (W) is given by the equation:
W = F × d
where F is the force exerted and d is the distance moved.
In this case, the force (F) exerted by the elevator is equal to the weight (Wt) of the elevator, which can be calculated using the equation:
Wt = m × g
where m is the mass of the elevator and g is the acceleration due to gravity.
Given that the elevator weighs 2080 lb, we need to convert this to mass by dividing by the acceleration due to gravity (32.2 ft/s^2):
m = 2080 lb / 32.2 ft/s^2
Next, let's calculate the distance (d) moved by the elevator. The distance is given as 200 ft.
Now, we can calculate the work done by the motor:
W = F × d = (m × g) × d
Next, let's calculate the power (P) output of the motor. Power is the rate at which work is done and is given by the equation:
P = W / t
where t is the time taken to do the work.
Given that the motor has a power output of 100 hp, we need to convert this to Watts:
P = 100 hp × 746 W/hp
Thus, the work done by the motor is equal to the power output multiplied by the time taken:
W = P × t
Lastly, to find the energy lost during the 10-second period, we need to find the efficiency (η) of the motor. Efficiency is given by the equation:
η = Work output / Work input
Energy lost = (1 - η) × Work input
Substitute the values we found earlier into the equations to calculate the energy lost during the 10-second period.