Two buckets of sand hang from opposite ends of a rope that passes over an ideal pulley. One bucket is full and weighs 110 N; the other bucket is only partly filled and weighs 50 N .

Initially, you hold onto the lighter bucket to keep it from moving. What is the tension in the rope?

You release the lighter bucket and the heavier one descends. What is the tension in the rope now?

Eventually the heavier bucket lands and the two buckets come to rest. What is the tension in the rope now?

Can anyone help me i've been doing this all night?

m=mass of partly filled bucket=6.3kg

M=Mass of filled bucket=10.3kg

ma=T-63
Ma=103-T

ma+63=103-Ma
a=(103-63)/(M+m)=2.41

Plug a back into one of the original equations we solve for T:
T=ma+63=(6.3)(2.41)+63=78.2
2 years ago

I can help with that! Let's go through each of the situations step by step:

1. Initially, you are holding the lighter bucket, so it doesn't move. The tension in the rope is equal to the weight of the heavier bucket, which is 110 N.

2. When you release the lighter bucket, the heavier bucket starts to descend. In this situation, the tension in the rope is equal to the difference in weight between the two buckets. So the tension in the rope is 110 N (weight of the heavier bucket) minus 50 N (weight of the lighter bucket) which equals 60 N.

3. Eventually, the heavier bucket lands and both buckets come to rest. At this point, the tension in the rope becomes zero since there is no force pulling on either end of the rope.

I hope this helps!

Sure, I can help you with that!

To determine the tension in the rope, we need to consider the forces acting on the buckets.

1. Initially, when you hold onto the lighter bucket, the tension in the rope is equal to the weight of the heavier bucket. The tension in the rope is 110 N because the weight of the heavier bucket is 110 N.

2. When you release the lighter bucket and the heavier one descends, the tension in the rope is the difference between the weights of the two buckets. The tension in the rope is 60 N because the weight of the heavier bucket is 110 N and the weight of the lighter bucket is 50 N.

3. Eventually, when the heavier bucket lands and both buckets come to rest, the tension in the rope becomes zero. This is because there is no upward force acting on the buckets once they come to rest.

So, to summarize:

1. Initially: Tension in the rope = Weight of heavier bucket = 110 N
2. When heavier bucket descends: Tension in the rope = Weight of heavier bucket - Weight of lighter bucket = 60 N
3. After both buckets come to rest: Tension in the rope = 0 N

I hope this explanation helps! If you have any further questions, feel free to ask.