Question

The figure shows an elaborate setup of a blue cord wrapped around six pulleys supporting three weights (two of which have identified weight in N, one of which is not given). The pulleys are supported by the red cables from the ceiling which are labeled with numbers 1-4. The blue cord is attached to the ceiling at its right end, but attached to one of the pulleys at its left end. The weights are suspended from the pulleys using pink cables. Give the following answers using the drop-down lists:

1. What is the tension in the blue cord (in N)?

2. What is the unknown weight (in N)?

3. One of the four red support cables has less tension than the others. Which one?

4. In the red cable that has the minimum tension, what is that value of tension (in N)?

@ @ @ @ 200N 120 N

Answer 1

Solution

Since the pulleys are at rest we can pick one pulley at a time and solve it. Again, we should be clever about which pulley to pick and we will obviously choose the pulleys with minimum variables.

Note: the tension in a cord when it is at rest is same throughout it. As if it had different tension at different point the rope would be accelerating towards that point

1)

We take the pulley with 120kg weight

So, there is only one variable here which is the tension of the blue string

The equation is

T+T = 120

2T = 120N

T= 60N , which is the tension of the blue string

2)

For the unknown mass "x", we see that the blue string is attached to it in 3 places

So, T+T+T = x

3T = x

x=3*60 = 180 N, which is the unknown weight

3)

For this we can visualize or we can do the math. We will do both here

First math

for pulley 1

T₁ = 2T = 120N

for pulley 2

T₂ = 2T = 120N

for pulley 3

T₃ = 2T = 120N

for pulley 4

T₄ = 200 -2T = 80N, which is also the answer number 4.

so answer is the red cord number 4

We can also visualize by seeing the number of strings attached to it. For the other pulleys we fing 3 strings : 2 blue 1 red

but for pulley 4 we see 2 blue 1 red and 1 pink. So, this is the only pulley with different combination.

If any doubt feel free to comment