A box of mass 18 kg is pulled at a steady speed across a floor by a rope at 28° above the…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A box of mass is pulled at a steady speed across a floor by a rope at above the horizontal. The coefficient of kinetic friction is . Taking :
- What is the tension in the rope?
- What is the normal reaction?
Need a reminder? The key ideaShow
Static friction matches the push, up to a limit . Once the body slides, kinetic friction is , nearly steady, with . Friction acts along the surface, against the sliding.
The normal reaction is the push of a surface, at right angles to it. It is only as big as it needs to be: find it from the forces across the surface, which balance if the body does not move off the surface.
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. Steady speed, so the forces balance both along and across the floor.
Step 1. Across the floor. .
Step 2. Along the floor. .
Step 3. Solve. , so .
Step 4. Normal reaction. .
Answer: (a) . (b) .
Check. A horizontal rope would need . The slanting rope needs only a little more, because it also lightens the box.
Watch out. Taking ignores the rope's lift and gives too much friction.
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