Q1.
You can place the box on a smooth inclined plank as shown in (Fig. 7.26b), and push the box up the plank to the platform. Does this method require a smaller force?
Answer
Yes. Pushing the box up a smooth ramp needs a smaller force than lifting it straight up — smaller by the factor h/L.
Lifting straight up: force needed = weight = mg, distance = h
Pushing up a ramp of length L to the same height h at constant speed:
work you do = F′ × L
potential energy gained = mgh
Work–energy theorem (ignoring friction): F′ × L = mgh
F′ = mgh / L = mg × (h/L)
Since L > h, the factor h/L is less than 1, so F′ < mg
Pushing up a ramp of length L to the same height h at constant speed:
work you do = F′ × L
potential energy gained = mgh
Work–energy theorem (ignoring friction): F′ × L = mgh
F′ = mgh / L = mg × (h/L)
Since L > h, the factor h/L is less than 1, so F′ < mg
For example, raising a 100 kg crate through h = 1 m using a ramp of length L = 4 m:
Lifting directly: F = mg = 100 kg × 10 m s–2 = 1000 N
Up the ramp: F′ = 1000 N × (1 m / 4 m) = 250 N — only a quarter as much
Up the ramp: F′ = 1000 N × (1 m / 4 m) = 250 N — only a quarter as much
Why it is not "free": the work done is the same both ways — 1000 J in this example. On the ramp you apply 250 N over 4 m instead of 1000 N over 1 m. The machine spreads the same work over a longer distance so that the force at any instant is small enough for you to manage.