Q1.
Next, place the plank against the top of the pile of books or stool as shown in Fig. 7.27a. Pull the cart along the plank slowly and steadily. Is the reading of the spring balance (the force required) smaller than that of step 2?
Answer
Yes — the spring balance reads clearly less on the ramp than when the cart was lifted straight up.
| How the cart is raised | Spring balance reads | Distance moved | Work done |
|---|---|---|---|
| Step 2 — lifted vertically through h = 0.5 m | mg (full weight) | 0.5 m | mg × 0.5 m |
| Step 3 — pulled up a plank of length L = 1.5 m | mg × (h/L) = mg/3, i.e. about one-third | 1.5 m | (mg/3) × 1.5 m = mg × 0.5 m — same |
Mechanical advantage of the plank = L / h = 1.5 m / 0.5 m = 3
So the effort is one-third of the weight.
If the cart weighs 6 N, the balance should read about 2 N on the ramp.
So the effort is one-third of the weight.
If the cart weighs 6 N, the balance should read about 2 N on the ramp.
Why it happens: the plank supports part of the cart's weight through the normal force. You only have to overcome the component of the weight that acts along the slope, and the gentler the slope, the smaller that component is.
Check it yourself: measure the actual reading. It will be a little more than mg × h/L, because friction between the cart's wheels and the plank has to be overcome too — the derivation above ignores friction.