A crane lifts a load of mass 6.4 kg on a rope.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A crane lifts a load of mass on a rope. Taking , what is the tension in the rope when the load
- hangs at rest;
- accelerates upward at ;
- accelerates downward at ?
Need a reminder? The key ideaShow
Draw a free-body diagram: the body alone, with every force on it. Then apply along the motion. For a body hanging from a rope or standing on a scale, with up positive:
What matters is the direction of the acceleration, not of the motion.
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. , .
Plan. Two forces act on the load. With up positive, , so .
Step 1. At rest. : .
Step 2. Accelerating up. .
Step 3. Accelerating down. : .
Answer: (a) . (b) . (c) .
Check. The rope pulls harder than the weight to speed the load up, and less to let it speed up downward. Good.
Watch out. A load moving up while slowing down is also accelerating downward. It is the acceleration that decides.
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