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A 1.2 kg trolley is at rest. A force on it rises steadily from 0 N to 30 N in 0.16 s, then falls…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A trolley is at rest. A force on it rises steadily from to in , then falls steadily back to in the next . The force acts along the track.
- What impulse does the force give?
- What is the trolley's speed afterwards?
Need a reminder? The key ideaShow
Momentum is , a vector. A force acting for a time changes it. The change is the impulse:
Choose a positive direction and give every velocity its sign. For a force that changes with time, the impulse is the area under the force-time graph.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. Peak force ; the force lasts in all; , .
Plan. The impulse is the area under the force-time graph, a triangle here.
Step 1. Area. .
Step 2. Speed. , so .
Answer: (a) . (b) .
Check. The average force is half the peak, , for : . It agrees.
Watch out. Using the peak force for the whole time doubles the answer. Only a steady force can be multiplied by the time directly.
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