Spring scale A is attached to the floor and a rope runs vertically upward, loops over the pulley, and runs down on the other side to a 99 N weight as shown (in original problem). Scale B is attached to the ceiling and the pulley is hung below it. What are the readings of the two spring scales, A and B? Neglect the weights of the pulley and scales.
I already found that scale A reads 99 N, but stuck on B.
B? well, the two ropes around the pulley both have 99 pulling on it, so the ceiling must be 2*99. At the pulley, force up= force down.
To find the reading of scale B, we can analyze the forces acting on it.
First, let's consider the weight attached to scale B, which is 99 N. This force acts downward.
Since the pulley is hung below scale B, it exerts an upward force equal to the weight attached to it, which is also 99 N. This cancels out the weight of the pulley, so we can ignore its effect.
Therefore, the total force acting upward on scale B is 99 N. As a result, the reading on scale B will be 99 N.
So, the readings of the two spring scales are:
- Scale A: 99 N
- Scale B: 99 N
To find the reading of spring scale B, we need to consider the forces acting on the system.
Let's analyze the forces on each side of the pulley separately:
On the side with scale A:
- The weight attached to scale A pulls downward with a force of 99 N.
On the side with scale B:
- The weight attached to scale B hangs downward with a force of 99 N.
- The tension in the rope pulling upward is the same on both sides of the pulley. Let's call this tension force T.
Since there is no acceleration in the system (it is in equilibrium), the sum of the forces on each side of the pulley should be equal:
On the side with scale A:
- Force downward due to the weight = 99 N
On the side with scale B:
- Force upward due to the tension in the rope = T
- Force downward due to the weight = 99 N
Therefore, we can write the equation:
T - 99 N = 99 N
By solving the equation, we can find the tension force T and, subsequently, determine the reading of scale B.
T - 99 N = 99 N
T = 99 N + 99 N
T = 198 N
So, the reading of spring scale B is 198 N.