A couple of basic physics problems

[ucsbjosh]

a couple of "basic" physics problems

i am stuck on a couple of my homework problems for my "basic" physics class. any help with either of them would be greatly appreciated.

1. a window washer pulls herself up in a bucket-pulley apparatus (single massless, frictionless pulley). how hard must she pull downward (on the rope end) to raise herself slowly at constant speed? the mass of the person and the bucket is 67 kg.

i am not sure how to get started on this problem, i think that the bucket is being pulled down by gravity with the force mg, and that to slowly raise herself at a constant speed she would need to pull with slightly more force than that, but i can't seem to get the right answer.

2. the two masses, m1 = 2.10 kg and m2 = 3.20 kg shown in the figure below, are each initially h1 = 1.56 m above the ground, and the massless, frictionless pulley is fixed h2 = 4.84 m above the ground. suppose the pulley is suspended by a cord to the ceiling. what is the tension in this cord after the mass is released and before it hits the ground? (i have attached the figure)

when i try to work this problem, i understand that the masses are both accelerating at the same rate, with m1 going up (y+) and m2 going down (y-) and that while they are in this state, they put a force downward on the pulley, which in turn puts a tension into the rope. i am not sure how to find the tension in that rope that is suspending the pulley from the ceiling.

again, any help with either of these problems would be greatly appreciated, thanks in advance.

josh

 

[HallsofIvy]

1. The window washer is also standing on the platform. The weight she needs to lift (and so the force she needs to exert) is the sum of the weights of herself and the bucket.

2. Yes.The heavier weight will go down, pulling the lighter weight upward. The force necessary to do that (the difference between between the weights) is the force the rope is exerting on the pully and, since the pully is not moving, the force the pully is exerting on the rope: that is the tension in the rope.

 

[wais]

For the first problem, you are correct in thinking that the bucket is being pulled down by the force of gravity, which is equal to the mass (67 kg) multiplied by the acceleration due to gravity (9.8 m/s^2). In order for the person to raise themselves at a constant speed, they would need to exert a force equal to the weight of the bucket plus themselves, or 67 kg x 9.8 m/s^2 = 656.6 N. This would be the minimum force required to raise themselves at a constant speed, but they may need to pull with slightly more force due to friction in the pulley system.

For the second problem, you can use Newton's second law (F=ma) to find the acceleration of the masses. Since they are connected by a rope, they will have the same acceleration. Once you have the acceleration, you can use the equations of motion (d=vi*t+1/2at^2) to find the time it takes for the masses to hit the ground. Then, using the equation for tension in a rope (T=ma), you can find the tension in the rope before the mass hits the ground.

Remember to keep track of the direction of the forces and accelerations, as they will affect the signs in your calculations. It may also be helpful to draw a free-body diagram for each mass to visualize the forces acting on them. Good luck with your homework!