Maximizing Potential Energy in a Falling Mass-Spring System

In summary, the problem involves a 10-g mass attached to a vertical spring with a spring constant of 49 N/m being dropped and the potential energy due to the spring and gravity is considered. The maximum speed of the falling mass and the distance it drops before coming to rest momentarily is calculated using the conservation of energy equation. The potential energy of the spring with the mass attached is also taken into account, and the KE is isolated and solved for the value of y that maximizes it.
  • #1
Rhaen
5
0
Hello all, I am looking for some assistance with a physics problem that I have for my physics class. Any help would be greatly appreciated because I have no idea where to start. Thank you all ahead of time for your help.

The problem is:
A 10-g mass is attached to the end of an unstressed, light,
vertical spring (k = 49 N/m) and then dropped. Answer the
following questions by considering the potential energy due
to the spring plus the potential energy due to gravity, i.e.
measure distances from the equilibrium position of the spring
with no mass attached. (a) What is the maximum speed of the
falling mass? (b) How far does the mass drop before coming
to rest momentarily? (c) Repeat (a) and (b), but answer the
questions by considering the potential energy of the spring
with the mass attached, i.e. measure distances from the
equilibrium position of the spring with the mass attached.

I don't even know how to start with the problem so any help would be most appreciated.

-Rhaen-
 
Physics news on Phys.org
  • #2
Ok so far all I have been thinking I could do with part a is this...

(a)
(1/2)mv^2 + mg(y_1-y_2) = (1/2)mv^2 + mg(y_1-y_2)

This comes from the equation K_1 + U_1 = K_2 + U_2

I don't know if I am missing something in that equation though. I know that there will be cancelations, I think the U_2 and K_1 possibly, but I'm not sure exactly how I would calculate the velocity out of that equation. Thank you for any light you can shine on this.

-Rhaen-
 
  • #3
Don't forget spring potential energy: 1/2 k y^2

Now apply conservation of energy:
KE_1 + GPE_1 + SPE_1 = KE_2 + GPE_2 + SPE_2

Hint: Given the initial speed and your reference point for measure PE, all the terms on the left are zero.
 
  • #4
So then the equation qould go:

0 = (1/2)mv^2 + mg(y_1-y_2) + (1/2)ky^2
0 = (.1kg)v^2 + (.2kg)(9.8)(y_1-y_2) + (49)y^2

If that is the case then how would I calculate the y distance so that I can have only the variable for velocity remaining? Thank you for your time.

-Rhaen-
 
  • #5
I would write the equation like this:
0 = (1/2)mv^2 + mgy + (1/2)ky^2

You are measuring the potential energy from the y=0 (unstretched) point. Now isolate the KE to one side, giving KE as a function of y. The find what value of y maximizes the KE. (The answer will be some negative value for y.)
 

1. What is a spring?

A spring is a flexible object, typically made of metal, that can be stretched or compressed and will return to its original shape when the force is removed.

2. How does a spring store energy?

A spring stores energy in the form of potential energy. When a force is applied to stretch or compress the spring, the potential energy is stored in the bonds between the atoms of the material. This energy is released when the spring returns to its original shape.

3. What factors affect the amount of energy stored in a spring?

The amount of energy stored in a spring is affected by the material it is made of, the dimensions of the spring, and the amount of force applied to stretch or compress it. A stiffer spring made of a stronger material will store more energy than a weaker spring made of a more flexible material.

4. How is the energy stored in a spring related to its potential energy?

The energy stored in a spring is equal to its potential energy, which is calculated using the formula PE = 1/2kx^2, where k is the spring constant and x is the displacement of the spring from its equilibrium position.

5. What are some real-life applications of springs and spring energy?

Springs and spring energy are commonly used in various devices, such as mattresses, trampolines, and door hinges. They are also essential components in mechanical systems, such as car suspensions and shock absorbers, where they help to absorb and store energy to reduce the impact of bumps and vibrations.

Similar threads

  • Introductory Physics Homework Help
Replies
29
Views
784
  • Introductory Physics Homework Help
Replies
5
Views
736
  • Introductory Physics Homework Help
Replies
17
Views
213
  • Introductory Physics Homework Help
Replies
20
Views
2K
  • Introductory Physics Homework Help
Replies
13
Views
195
  • Introductory Physics Homework Help
Replies
24
Views
837
  • Introductory Physics Homework Help
Replies
17
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
394
  • Introductory Physics Homework Help
Replies
12
Views
1K
  • Introductory Physics Homework Help
Replies
31
Views
947
Back
Top