Two springs and the energy question

In summary: You need to find the amount that each spring will stretch when pulled back to the given position (x=0.7m). You also need to consider that each spring will provide half of the total force needed to hold the stone at that position.
  • #1
coldpay
5
0

Homework Statement



A horizontal slingshot consists of two light, identical springs (with spring constants of 24.1 N/m) and a light cup that holds a 1.21-kg stone. Each spring has an equilibrium length of 50 cm. When the springs are in equilibrium, they line up vertically. Suppose that the cup containing the mass is pulled to x = 0.7 m to the left of the vertical and then released. Determine

a) the system’s total mechanical energy.


b) the speed of the stone at x = 0.




Homework Equations





The Attempt at a Solution

 

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  • #2
welcome to pf!

hi coldpay! welcome to pf! :wink:

show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 
  • #3
i know the the total mechanical energy is mgh plus 0.5kx^2 but i can't find the answer.

answers
a)3.127 J
b)2.274 m/s
 
  • #4
coldpay said:

Homework Statement



A horizontal slingshot consists of two light, identical springs (with spring constants of 24.1 N/m) and a light cup that holds a 1.21-kg stone. Each spring has an equilibrium length of 50 cm. When the springs are in equilibrium, they line up vertically. Suppose that the cup containing the mass is pulled to x = 0.7 m to the left of the vertical and then released. Determine

a) the system’s total mechanical energy.


b) the speed of the stone at x = 0.




Homework Equations





The Attempt at a Solution


coldpay said:
i know the the total mechanical energy is mgh plus 0.5kx^2 but i can't find the answer.

answers
a)3.127 J
b)2.274 m/s

I don't think the mgh term will change by pulling back the slingshot. Calculate how much energy is stored in the springs as they are pulled from their equilibrium postition back to the position shown. Show us your work please.
 
  • #5
X=√0.5^2+0.7^2=0.86

0.5kx^2=0.5*48.2*(0.86)^2=17.34 i found this but i am not sure if the spring is parallel or serial(i take it parallel)

This is all i can do.I don't know the rest of the question.
 
  • #6
coldpay said:
X=√0.5^2+0.7^2=0.86

0.5kx^2=0.5*48.2*(0.86)^2=17.34 i found this but i am not sure if the spring is parallel or serial(i take it parallel)

This is all i can do.I don't know the rest of the question.

In the spring equation, the "X" is meant to be the amount of stretch, not the overall length.
 

FAQ: Two springs and the energy question

What is the concept of two springs and the energy question?

The concept of two springs and the energy question is a physics problem that involves two springs connected in series. The problem aims to determine the energy stored in each spring and the total energy of the system.

How do you calculate the energy stored in each spring?

To calculate the energy stored in each spring, you can use the formula: E = 1/2kx^2, where E is the energy, k is the spring constant, and x is the displacement from the equilibrium position. You will need to calculate the energy for each spring separately and add them together to get the total energy of the system.

What happens to the energy when the springs are connected in series?

When the springs are connected in series, the energy is shared between the two springs. This means that the total energy of the system is divided between the two springs, and each spring will have a fraction of the total energy.

How do you determine the total energy of the system?

The total energy of the system can be determined by adding the energy stored in each spring together. This means that Etotal = E1 + E2, where Etotal is the total energy, E1 is the energy stored in the first spring, and E2 is the energy stored in the second spring.

What is the relationship between the spring constant and the energy stored in the spring?

The spring constant and the energy stored in the spring have a direct relationship. This means that as the spring constant increases, the energy stored in the spring will also increase. Similarly, if the spring constant decreases, the energy stored in the spring will decrease.

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