Suggestion:
Consider the FBD shown above for the cart, person and three cut ends of the rope. Using Newton's second law on an axis along the incline will give you one equation for the acceleration of the cart/man.
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6 comments:
Is each 'T' the same force that exerted by the man?
or does the sum of three T's equal to the amount of that person exerting since it's the only force moving the cart?
Problem resolved.
I realized that each 'T' indicates the force exerted by the person. The problem says that the man exerts 'x' amount of force on the rope, and this means that the same amount of force is applied through out the entire rope.
isn't it right?
-GeunHo
this is me participating
Anonymous, Yes
I dont understand here why we would count T=60 lbs three times and all in the same direction ?
By definition, an FBD is a Diagram of the Body that is cut Free from its environment where its environment is replaced by the forces acting on the body by the environment. With this particular choice of cuts, we have exposed three free ends of the cable. We are given that the man exerts 60 lb on one end of the exposed cable. The forces at the other two cuts must be the same since smooth, massless pulleys change only the direction of the force, not the magnitude. As a result, there are three, 60-lb forces acting on the FBD along the incline.
This is a good example of how important that the FBD is in solving kinetics problems. This result might not immediately match up with your intuition. However, this force multiplication is the fundamental idea behind a cable-pulley system and is readily seen from the FBD.
Good question.
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