A 1.5 kg cart moves along the x axis at 2.0 m/s when it passes x = 1 m.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A cart moves along the axis at when it passes . From there a force newtons (with in metres) pushes it along the axis.
- How much work does the force do between and ?
- How fast is the cart moving at ? Ignore friction.
Need a reminder? The key ideaShow
The work of a force that changes along the path is the area under its force-position graph, . For a spring, .
Kinetic energy is . The work-energy theorem: the net work done on a body equals its change in kinetic energy, .
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. , at ; .
Plan. Integrate the force for the work, then use the work-energy theorem.
Step 1. Work. .
Step 2. Energy at the start. .
Step 3. Speed. , so and .
Answer: (a) . (b) .
Check. The force runs from to over , so the work must lie between and . It does.
Watch out. Using (its value at the end) for the whole way overstates the work: the force was smaller earlier.
Discussion (0)
Log in to join the discussion.
Loading…