What is the equation for the object's velocity after being pushed in spring?

  • Thread starter Thread starter Zero
  • Start date Start date
  • Tags Tags
    Spring
Click For Summary

Homework Help Overview

The discussion revolves around determining the velocity of an object after it has been pushed by a spring, considering the effects of friction and energy conversion. The subject area includes concepts from mechanics, specifically energy conservation and kinematics.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the conversion of potential energy from the spring into kinetic energy and the impact of friction on the object's motion. There are attempts to calculate deceleration due to friction and to apply kinematic equations to find the final velocity. Questions arise about the validity of using certain formulas and the implications of negative values in calculations.

Discussion Status

Participants are actively engaging with each other's reasoning, exploring different interpretations of the problem. Some guidance has been offered regarding the application of kinematic equations and the role of initial velocity. However, there is no explicit consensus on the correct approach or final answer.

Contextual Notes

There are constraints related to the initial conditions of the problem, such as the initial velocity being considered as zero and the effects of friction only becoming relevant after the object leaves the spring. Participants are also working with specific energy values provided in the discussion.

Zero
Messages
17
Reaction score
4
Homework Statement
Problem: A spring is compressed 50 cm from the equilibrium position. The spring constant is 12 N/cm. A 20 kg object is placed next to the spring initially at rest and it is released. After the object is released from the spring, the force of friction acting on the object is 30 N.

A) Calculate the force required to compress the spring by 50 cm. (Already got the answer which is 600N)

B) Calculate the energy that was stored in the spring. (Got this answer also which is 150 J)

C. Calculate the object's velocity 4m after it has left the spring. (This is where I stopped don't know what to do here)

What I tried: Unfortunately I don't know where to begin. I know what variables are which are work, spring constant, friction and potential energy in the spring which is the same as the work.

As for number 3, I'm totally lost but I do have a theory that I don't know if it would be true for this specific equation.

Theory: Would I have to find kinetic energy first.

The reason that I have such a theory is because of question D which I did not add since I did not attempt it as of yet but as of posting this, I will be attempting.
Relevant Equations
F=Kx and W=1/2FX
Et1+w=Et2
1/2mv+w=1/2mv
0+150=1/2 (20)
300=(20)v
15=v
I know this answer is wrong.
 
Physics news on Phys.org
When the object leaves the spring, the energy that was stored in the spring is converted into the kinetic energy of the object. So you can calculate the speed of the object at the time when it first leaves the spring. You are told that "After the object is released from the spring, the force of friction acting on the object is 30 N." Calculate the deceleration from that.
 
I did what would you said and got -1.5003 m/s^2 but when I use the formula final velocity squared=initial volocity+two (acceleration)(distance) I couldn't do it because I can't square root a negative number. Is the formula used wrong or am I on the right track but I just forgot a very key detail. Also, I did get the kinetic energy of the object at 4m which is 30J
 
Zero said:
I did what would you said and got -1.5003 m/s^2 but when I use the formula final velocity squared=initial volocity+two (acceleration)(distance) I couldn't do it because I can't square root a negative number. Is the formula used wrong or am I on the right track but I just forgot a very key detail. Also, I did get the kinetic energy of the object at 4m which is 30J
Can you show your equation? Just because the velocity is decreasing and doesn't reach zero, doesn't mean that you need to take the square root of a negative number...
 
Zero said:
final velocity squared=initial volocity+two (acceleration)(distance)
That should be
final velocity squared=initial velocity squared + two (acceleration)(distance)
What did you get for initial velocity?
Zero said:
I did get the kinetic energy of the object at 4m which is 30J
So deduce the velocity from that.
 
haruspex said:
That should be
final velocity squared=initial velocity squared + two (acceleration)(distance)
What did you get for initial velocity?

So deduce the velocity from that.
isn't initial velocity 0 so it wouldn't matter. Yes i know the kinetic energy is 30j and the velocity is 1.73 m/s but i just don't know how to get the answer for velocity unless you did a different formula than Ek=1/2mv^2 to find kinetic energy then that is possible to deduce that way
 
Zero said:
isn't initial velocity 0 so it wouldn't matter.
The acceleration in the equation you are using results from friction, and that does not start until the object leaves the spring. So for this equation the initial velocity is the velocity as it leaves the spring.
 
  • Like
Likes   Reactions: berkeman
haruspex said:
The acceleration in the equation you are using results from friction, and that does not start until the object leaves the spring. So for this equation the initial velocity is the velocity as it leaves the spring.
Got the answer thank you all for the effort
 
  • Like
Likes   Reactions: berkeman
berkeman said:
Can you show your equation? Just because the velocity is decreasing and doesn't reach zero, doesn't mean that you need to take the square root of a negative number...
Got the answer thank you all for the effort
 
  • Like
Likes   Reactions: berkeman

Similar threads

The value of the spring constant k that I calculate seems too high
  • · Replies 11 ·
Replies
11
Views
1K
A cart collides with a bumper -- Find the final displacements, etc.
  • · Replies 15 ·
Replies
15
Views
2K
Finding a formula for displacement of a mass on a spring using v.
  • · Replies 2 ·
Replies
2
Views
924
What average power does the boy need to produce?
  • · Replies 12 ·
Replies
12
Views
1K
A Spring pushing an object up a 25 cm slope
  • · Replies 6 ·
Replies
6
Views
1K
Finding the energy lost in a collision as the bullet collides to the block
  • · Replies 12 ·
Replies
12
Views
3K
Two bars connected by a spring on a floor with friction
  • · Replies 37 ·
2
Replies
37
Views
2K
Easy conservation of energy problem? (long jump)
  • · Replies 5 ·
Replies
5
Views
3K
Elastic potential energy (spring) problem
  • · Replies 3 ·
Replies
3
Views
2K
Conservation of Energy of cart Problem
  • · Replies 5 ·
Replies
5
Views
5K