Find Stretch of Each Spring After Cutting 100-Coil Spring

In summary, when a 100-coil spring with an object attached to the lower end is cut into two identical 50-coil springs, each spring will stretch by 0.0775 m. This is due to the fact that each spring carries half of the mass, resulting in a decrease in the spring constant and an increase in the displacement. The final answer is 0.0387 m for each spring.
  • #1
huskydc
78
0
An object is attached to the lower end of a 100-coil spring that is hanging from the ceiling. The string stretches by 0.155 m. The spring is then cut into two identical springs of 50 coils each. As the drawing shows, each spring is attached between the ceiling and the object. By how much does each spring stretch?
 
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  • #2
Have any thoughts?
 
  • #3
well, since the mass is carried by two springs, each spring carries half the mass...but that's all i know... =(
 
  • #4
100:0.115 = 50:x

x = .115/2
 
  • #5
sorry plucker, but that's not the right answer. again, i drew another FBD,
for one spring: F(spring) = mg

k = mg/x(1)

for 2 springs: 2F(spring) =mg
2 k x(2) =mg

but with only x(1) known, and no mass, how should i approach this?


...ok, after some tries..
i somehow found the right answer as .0387. but does anyone want to explain the concepts behind it?
 
Last edited:

1. How do I find the stretch of each spring after cutting a 100-coil spring?

To find the stretch of each spring, you will need to use Hooke's Law, which states that the force applied to a spring is directly proportional to the distance it stretches. First, measure the length of the original 100-coil spring and record it as "L". Then, cut the spring into the desired number of smaller springs and measure the length of one of the smaller springs, recording it as "l". Finally, plug these values into the equation F = kx, where F is the force applied, k is the spring constant, and x is the distance the spring stretches. Solve for the spring constant and plug it into the equation x = (F/k) * (l/L) to find the stretch of each spring.

2. What is Hooke's Law and how does it relate to finding the stretch of each spring?

Hooke's Law is a principle in physics that states that the force applied to a spring is directly proportional to the distance it stretches. This means that as the force applied to a spring increases, the distance it stretches also increases. By using this law and plugging in the necessary values, we can calculate the stretch of each spring after cutting a 100-coil spring.

3. Can I use any spring to find the stretch after cutting a 100-coil spring?

Yes, as long as the spring is made of a material that follows Hooke's Law, you can use any spring to find the stretch after cutting a 100-coil spring. However, it is important to note that different materials have different spring constants, so the calculated stretch may vary.

4. Are there any other factors that may affect the stretch of each spring?

Yes, there are other factors that may affect the stretch of each spring, such as the diameter of the wire used to make the spring, the number of coils in each spring, and the amount of force applied. It is important to keep these factors constant when conducting the experiment to ensure accurate results.

5. Is there a specific method for cutting the 100-coil spring into smaller springs?

There is no specific method for cutting the 100-coil spring into smaller springs, but it is important to make clean and precise cuts to ensure that each smaller spring has the same number of coils. Using a sharp tool, such as wire cutters, and measuring the length of each smaller spring can help to achieve accurate results.

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