A crane lifts a mass m to the 10th floor of a building in a certain time. Class 9

A crane lifts a mass m to the 10th floor of a building in a certain time. Class 9

Question 1.

A crane lifts a mass m to the 10th floor of a building in a certain time. It then raises the same mass to the 20th floor of the same building in double the time. How much more energy and power are required? Assume that the height of all floors is equal. Class 9

Answer:

Let height of each floor = d. Time to 10th floor = t; time to 20th floor = 2t.

1. Energy to 10th floor: E₁ = mg × 10d
2. Energy to 20th floor: E₂ = mg × 20d = 2 × E₁ (twice the energy required)
3. Power to 10th floor: P₁ = E₁/t
4. Power to 20th floor: P₂ = 2E₁/(2t) = E₁/t = P₁ (same power required)

Lifting to the 20th floor requires twice the energy but the same power as lifting to the 10th floor.