Equal forces, unequal motion
A spring pushes two carts apart with the same force. Do both carts move the same way?
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Step 1 of 3
- A light cart and a heavy cart, with a spring between them.
- Released: 120 N on each cart, in opposite directions.
- The light cart speeds off fast. The heavy cart barely moves.
No. The light cart speeds up more than the heavy cart.
The rule
The two forces of a pair are equal. They act on different objects, so they do not cancel. If nothing else pushes, the lighter object accelerates more.
Each object has its own calculation. For each, a = F ÷ m. The same F on a smaller m gives a bigger a.
If two equal, opposite forces act on the same object, they balance. The two forces of a pair never act on one object.
Think of two skaters on smooth ice, where friction is small.
| Case | Force on each | Accelerations |
|---|---|---|
| Two skaters, 60 kg and 40 kg, push apart | 30 N | Heavier: 30 ÷ 60 = 0.5 m/s². Lighter: 30 ÷ 40 = 0.75 m/s² |
| Earth and a dropped stone | Equal | The Earth's mass is huge, so its acceleration is too small to notice |