Question

How much work does an elevator motor do to lift a 2000 kg elevator a height of 120 m ? Express your answer with the appropriate units. Wext = nothing nothing Request Answer Part B How much power must the motor supply to do this in 59 s at constant speed? Express your answer with the appropriate units.

P= ____

Answer 1

The elevator motor does 2,352,000 J of work to lift the 2000 kg elevator 120 m. To do this in 59 seconds at constant speed, the motor must supply approximately 39.86 kW of power.

Step-by-step explanation:

The work done by the elevator motor to lift a 2000 kg elevator a height of 120 m is calculated using the formula Work (W) = Force (F) × Distance (d). Since the force needed to lift the elevator is equal to its weight, we use F = mg, where m is the mass (2000 kg) and g is the acceleration due to gravity (9.8 m/s2). So, W = 2000 kg × 9.8 m/s2 × 120 m, which equals 2,352,000 J (joules).

For part B, the power is work done over time. It is given by Power (P) = Work (W) / Time (t). Using the work calculated previously and time of 59 seconds, the power needed is P = 2,352,000 J / 59 s, which equals 39,864.41 W (watts), or approximately 39.86 kW (kilowatts).