Finding the Stopping Point of a Falling Mass on a Spring

In summary, the problem involves a 0.25 kg mass attached to a spring with a spring constant of 5.4 N/m, dropped from rest. The question asks for the point where it stops to the nearest hundredth of a meter. The correct answer is 0.91m, which is twice the stretch in its at rest equilibrium position. The solution involves using conservation of energy to show that its total stretch is twice the stretch in its at rest equilibrium position. The velocity is not needed to solve this problem.
  • #1
zachmgilbert
10
0

Homework Statement


A 0.25 kg mass is attached to a spring with spring constant 5.4 N/m and let fall. To the nearest hundredth of a meter what is the point where it 'stops'?

diagram here:
http://wps.prenhall.com/wps/media/objects/1088/1114633/ch11/grav.gif


Homework Equations


y=Asin(k/m)1/2t


The Attempt at a Solution


I don't know how to find t, or I am using the wrong equation.
 
Physics news on Phys.org
  • #2
What is going on(Force wise) when the mass reaches its lowest point?
 
  • #3
I tried F=-kx using mg for force. mg is (.25)(9.8) which equals 2.45. Dividing by 5.4 gave me .45 which is wrong. The correct answer is .91
 
  • #4
It is a giancoli problem so I can reset the variables. I've tried it multiples times and the F=-kx is always half of the correct answer. Where does it get multiplied by 2.
 
  • #5
Your equation assumes the weight is slowly lowered to its equilibrium position. In this case, however, it is dropped suddenly. Use conservation of energy to show that its total stretch is twice the stretch in its at rest equilibrium position.
 
  • #6
i have .5mv2=.5kx2 but i don't know how to find velocity.
 
  • #7
zachmgilbert said:
i have .5mv2=.5kx2 but i don't know how to find velocity.
The object starts from rest with no speed, and when it reaches the bottom, it momentarily stops and also has no speed. But there is gravitational potential energy at the top, and spring potential energy at the bottom.
 
  • #8
Thank You, that gave me the right answer.
 

Related to Finding the Stopping Point of a Falling Mass on a Spring

1. What is the stopping point of a falling mass on a spring?

The stopping point of a falling mass on a spring is the point at which the spring reaches equilibrium, meaning that the restoring force of the spring is equal to the force of gravity pulling the mass down.

2. How do you calculate the stopping point of a falling mass on a spring?

The stopping point can be calculated using the equation F = kx, where F is the force of the spring, k is the spring constant, and x is the displacement of the mass from its equilibrium position. When F = mg (force of gravity), the mass will reach its stopping point.

3. What factors affect the stopping point of a falling mass on a spring?

The stopping point is affected by the spring constant, the mass of the object, and the initial displacement of the mass from its equilibrium position. The stiffer the spring (higher spring constant), the higher the stopping point will be. A heavier mass will also result in a higher stopping point, while a larger initial displacement will result in a lower stopping point.

4. Can the stopping point be changed?

Yes, the stopping point can be changed by altering the factors that affect it. For example, the spring constant can be changed by using a different type of spring, or the mass and initial displacement can be adjusted to achieve a desired stopping point.

5. Why is it important to find the stopping point of a falling mass on a spring?

Knowing the stopping point is important in understanding the behavior of objects under the influence of forces, such as gravity and spring forces. It can also be useful in practical applications, such as designing and calibrating springs for suspension systems or determining the maximum weight a spring can support.

Similar threads

  • Introductory Physics Homework Help
Replies
24
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
877
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
8
Views
2K
  • Introductory Physics Homework Help
Replies
6
Views
873
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
26
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
4K
Back
Top