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a farmhand attaches a 25 kg bale of hay to one end of a rope passing over a frictionless pulley connected to a beam in a hay barn. another farmhand then pulls down on the opposite end of the rope with a force of 227 N. ignoring the mass of thr rope what will be the magnitude and direction of the ball's acceleration if the gravitational force acting on its 245 N?

  • physics -

    I would start by drawing a picture if you don't already have one because it's a bit hard to understand what's going on. Next, figure out what forces are acting on each side of the pulley. You have a gravitational force (245 N) pulling down on the hay ball and a force of tension pulling up. On the the other side you have a force (227 N) pulling down and the force of tension (the same as on the other side) pulling up. Once you figure this out you need to set up an equation that shows all the forces acting on the system (pulley and hay ball). Newton's second law says that the sum of forces on a system will equal ma and a is what you have to solve for. So the sum of forces on the side with the hay is T-G=ma where T is the force of tension and G is the force of gravity. Here, I am assuming that the ball is going to rise and making the forces towards the farmer positive. On the other side F-T=ma where F is the applied force from the farmer. Since there is no mass here the right side of the equation equals zero and you can deduce that F=T. Once you see this solving for a becomes a lot simpler. You can go back to the first equation and substitute F for T. Solve for a and you get (F-G)/m= a. When you solve it you get that a=-0.72 m/s squared. Which means that the hay ball is actually falling to the ground- the farmer isn't pulling it up.

    Hope this helps.

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