Two spring scales holding a hanging mass, what're the readings on both scales?

[gibbons530]

Having trouble with this tricky physics problem, anyone have an idea of what the answer would be?


1. Homework Statement

A 20-kg fish is weighed with two spring scales, each of negligible weight. What will be the readings on the scales?

A. Each scale will read 10 kg
B. Each scale will read 20 kg
C. The top scale will read 20 kg, and the bottom scale will read 0 kg
D. The bottom scale will read 20 kg, and the top scale will read 0 kg
E. Each scale will show a reading greater than 0 kg and less than 20 kg, but the sum of the two readings will be 20 kg

Homework Equations

Fnet = ma = Fg + Fsp1 + Fsp2 (+ T??)

The Attempt at a Solution

I'm going to be honest, I'm stumped on this one. I feel like the both spring forces will balance out the downward weight (w = mg). I think A makes the most sense, but I don't really know how to prove this is the correct answer using the formulas or a free-body diagram. I did draw the question out on MS Paint but I don't really know what else to add. Does the tension of the string play a key role in finding the answer? If anyone knows the answer and an explanation, it would be so helpful.

Thanks!
https://s.yimg.com/hd/answers/i/8fa9348e4cd54bf5b1fec3a8fbf55378_A.png?a=answers&mr=0&x=1411356970&s=78c197df753cb35bcf57e84d0ec4c158

 

[Simon Bridge]

Do you know the springs are one after the other like that?
If there were no springs - what would be the tension in the wire holding the fish up?
If there were one spring, what would be the tension in the wire holding the spring up?

Still stumped:
Draw a free body diagram for each spring, and the fish.

 

[gibbons530]

Yes, there are two spring scales, arranged like that. Our physics professor gave us a practice exam and that was what the picture looked like.

If there were no springs, then:
Fnet = T + -Fg = ma = 0
T - Fg = 0
T = Fg
T = (20kg)(9.8m/s2)
T = 196 N

For that free-body diagram, I drew a dot representing the fish, an upward arrow labeled T, and a downward arrow labeled Fg.

The springs are what are confusing me. When drawing a free-body diagram for the spring, would I have the spring be the mass? Would I draw Fspring and T upward, and Fg downward? Would T change due to the spring? I am pretty confused obviously, haha. Thanks for helping me though!

 

[Simon Bridge]

No - the problem statement says springs have negligible mass.
Make them a dot with tensions up and down from them.

Note: if a spring balance is pulled in opposite directions by the same force F, what force does the balance show?

 

[HalfLostAndSearching]

The correct answer is E. Each scale will show a reading greater than 0 kg and less than 20 kg, but the sum of the two readings will be 20 kg.

To understand why, let's break down the forces acting on the fish and the scales.

1. Weight of the fish (Fg = mg)
The fish has a mass of 20 kg, so its weight will be 20 kg * 9.8 m/s^2 = 196 N. This downward force is acting on both the fish and the scales.

2. Tension in the string (T)
The string is holding the fish and is under tension. This tension force is also acting on both the fish and the scales, but in opposite directions. The string is not negligible in weight, so we need to consider its tension force in our calculations.

3. Spring forces (Fsp1 and Fsp2)
Each spring scale is attached to the string and is pulling on it with a spring force. These forces are also acting in opposite directions. The top scale is pulling up with Fsp1, while the bottom scale is pulling down with Fsp2.

Now, let's look at the free-body diagrams for the fish and the scales.

Fish:
- There are two forces acting on the fish: its weight (Fg) and the tension in the string (T).
- Since the fish is not accelerating, the net force on it is zero. This means that Fg must be equal and opposite to T.
- Therefore, the tension in the string is also 196 N.

Top scale:
- There are three forces acting on the top scale: its weight (Fg), the tension in the string (T), and the spring force (Fsp1).
- Since the scale is not accelerating, the net force on it is zero. This means that Fg must be equal and opposite to T + Fsp1.
- Therefore, the reading on the top scale will be the sum of the tension force and the spring force, which is less than 196 N.

Bottom scale:
- There are three forces acting on the bottom scale: its weight (Fg), the tension in the string (T), and the spring force (Fsp2).
- Since the scale is not accelerating, the net force on it is zero. This means that Fg must be equal and opposite to T + Fsp2.
- Therefore, the reading on the