Question

For the following question, enter the correct numerical value up to TWO decimal places. If the numerical value has more than two decimal places, round-off the value to TWO decimal places. (For example: Numerical value 5 will be written as 5.00 and 2.346 will be written as 2.35) A mass of 50 kg is raised through a certain height by a machine whose efficiency is 90%, the energy spent is 5000 J. If the mass is now released, its KE on hitting the ground shall be _____ J

Hint:

In lifting problems, only the useful output energy (given by efficiency) converts into potential energy.

Answer 1

Correct Answer: 4500

Step 1: Efficiency of a machine is defined as \[ \text{Efficiency} = \frac{\text{Useful energy output}}{\text{Energy input}}. \]
Step 2: Given: \[ \text{Efficiency} = 90% = 0.9, \quad \text{Energy input} = 5000\,\text{J}. \] Useful energy gained by the mass (increase in potential energy): \[ PE = 0.9 \times 5000 = 4500\,\text{J}. \]
Step 3: When the mass is released, this potential energy is completely converted into kinetic energy just before hitting the ground (neglecting losses). \[ KE = PE = 4500\,\text{J}. \] Hence, the kinetic energy on hitting the ground is \[ \boxed{4500.00\,\text{J}}. \]