Which factors determine the energy required to raise a flag from the ground. Class 9

Which factors determine the energy required to raise a flag from the ground. Class 9

Question 1.

Which factors determine the energy required to raise a flag from the ground to the top of a tall flagpole using a pulley? Does raising the flag slowly or quickly change the amount of work done? If the speed at which the flag is raised is doubled, how does the power requirement change? Explain your answers. Class 9

Answer:

1. Factors determining energy: The energy required = mgh depends on (a) mass of the flag m, (b) acceleration due to gravity g, (c) height of the flagpole h. A fixed pulley only changes the direction of force, not the work required.
2. Does speed change work done? No. Work = mgh depends only on mass and height, not on speed. Whether raised slowly or quickly, the same work is done.
3. If speed is doubled: Time taken is halved (t/2). New power = mgh / (t/2) = 2 × (mgh/t) = 2P. The power requirement doubles when the speed is doubled.

Question 2.

A man of mass 60 kg rides a scooter of mass 100 kg. He accelerates the scooter to a velocity v. The next day, his son with a mass of 40 kg joins him as a passenger. If the scooter reaches the same speed on both days in the same time interval, what is the ratio of the fuel of the tank used on the two days? Assume that the energy transfer to the scooter happens entirely due to fuel, and no other losses occur due to air resistance and friction. Class 9

Answer:

1. Day 1: Total mass = 60 + 100 = 160 kg. KE₁ = 1/2 × 160 × v² = 80 v²
2. Day 2: Total mass = 60 + 100 + 40 = 200 kg. KE₂ = 1/2 × 200 × v² = 100v²

Since fuel used ∝ KE: Ratio of fuel used = KE₁ : KE₂ = 80v² : 100v² = 4 : 5