How is the Equilibrium Height of a Ball Determined Using Spring Constants?

Click For Summary

Homework Help Overview

The discussion revolves around determining the equilibrium height of a ball using two springs with known spring constants and initial lengths. The problem involves understanding the forces exerted by the springs and how they relate to the gravitational force acting on the ball.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the need to convert measurements from centimeters to meters and consider how to calculate the total force exerted by the springs. There are questions about how to apply the spring constants and the relationship between the forces of the springs and the gravitational force on the ball.

Discussion Status

Some participants have provided guidance on the relationship between the forces of the springs and the gravitational force. There is an ongoing exploration of how to combine the spring constants and apply them to find the equilibrium position, but no consensus has been reached on the final calculations.

Contextual Notes

Participants are working within the constraints of the problem statement, including the specific values of the spring constants and the mass of the ball. There is a focus on ensuring the correct application of the spring force equation and the overall setup of the problem.

dance_sg
Messages
113
Reaction score
0

Homework Statement


Two springs are set up on a table. The longer spring has a spring constant of 225 N/m and an initial length of 42.0 cm. The shorter spring has a spring constant of 675 N/m and an initial length of 28.0 cm. How far above the table is an 8.50-kg ball when it reaches its equilibrium position?


Homework Equations


f=-kx


The Attempt at a Solution


first change cm to m, then would i find the forces of each spring, add them up for find the total force, then use that and the 8.50 kg mass to find x?
 
Physics news on Phys.org


Yes, the springs combined must be equal to the gravitational force.
 


how exactly do i use the force that i found to solve for x? because i don't know k
 


k is the spring constant -- you have two springs and you know both their spring constants.
 


o! so just add the two up.
 


does this look right to you then?
F=-kx
F=(-225N/m x 0.42m)+(675N/m x 0.28m)
F=-94.5 + -189N
F= -283.5N
X=f/-k
X=-283.5N / -900N/m
X= 0.315
 

Similar threads

Replies
17
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 7 ·
Replies
7
Views
8K
Replies
7
Views
1K
Replies
16
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
3
Views
2K
Replies
3
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K