# Graphing Kinetic Energy of a Toy Car Released from a Compressed Spring

• sp3sp2sp
In summary, the toy car has a constant kinetic energy because its potential energy stays the same when the car's total energy increases.
sp3sp2sp

## Homework Statement

A toy car is held at rest against a compressed spring, as shown in the figure. When released, the car slides across the room. Let x=0 be the initial position of the car. Assume that friction is negligible.
Sketch a graph of the car's kinetic energy from the moment it is released until it passes the equilibrium position of the spring. Your graph should be consistent with the given plots of total energy (gray line in graphing window) and potential energy (gray parabola in graphing window).

Part A and B asked for total Energy and gravitational PE. This is shown in attached file. The problem is with plotting KE. I can't tell if I got it wrong because my graph is sloppy or if I actually have the shape completely wrong. The line that is marked wrong is the red line, which is supposed to be KE
thanks for any help

## Homework Equations

As PE decreases KE will increase, so that total E always constant. This is what I thought I plotted (?) thanks

## The Attempt at a Solution

#### Attachments

• KE AND PE.jpg
21.1 KB · Views: 8,582
sp3sp2sp said:

## Homework Statement

A toy car is held at rest against a compressed spring, as shown in the figure. When released, the car slides across the room. Let x=0 be the initial position of the car. Assume that friction is negligible.[/ATTACH]
As I read this problem statement, you have a flat floor and no friction. That being the case, why would the car ever slow down? Is that supposed to be due to wind resistance?

Just to clarify because it might be misunderstood.

Part A:Sketch a graph of the total energy of the spring and car system. There is no scale given, so your graph should simply reflect the qualitative shape of the energy vs. time plot.

Part B: Sketch a plot of the elastic potential energy of the spring from the point at which the car is released to the equilibrium position of the spring. Make your graph consistent with the given plot of total energy (the gray line given in the graphing window).

You have not answered my question

thank you for the reply. So because this is just from time car is released to when spring reaches its eq-position that means that car has acceleration and KE will increase but then be constant at springs eq-position (black line)?

#### Attachments

• KE AND PE2.jpg
23.2 KB · Views: 3,313
sp3sp2sp said:
thank you for the reply. So because this is just from time car is released to when spring reaches its eq-position that means that car has acceleration and KE will increase but then be constant at springs eq-position (black line)?
If I understand you correctly, then yes, that sounds correct.

No the car would not slow down. Problem says friction negligable

sp3sp2sp said:
No the car would not slow down. Problem says friction negligable
right. I misunderstood you. I think posts 5 and 6 clarify everything.

OK thanks but if you were to extend the graph (--> pos x) then would the KE simply = the total energy of the system?

sp3sp2sp said:
OK thanks but if you were to extend the graph (--> pos x) then would the KE simply = the total energy of the system?
Well, yeah, I suppose once the spring has done its thing, the only energy left in the system is the KE of the car. The energy of the system starts out as the energy of the coiled spring and that gets converted into the KE of the car.

I used all my answers up and they were all wrong. Then I clicked on show answer and it showed the graph that I originally got marked as wrong.

#### Attachments

16.5 KB · Views: 3,943
sp3sp2sp said:
I used all my answers up and they were all wrong. Then I clicked on show answer and it showed the graph that I originally got marked as wrong.
No, there's a difference.
In the PE graph, there are three kinks, so four straight sections.
In your failed attempt, the KE graph only has two kinks, so it is not an exact inversion of the PE graph.
The displayed correct version has the full three kinks.

I got this for an answer for the kinetic energy problem (last one). This is the correct answer

#### Attachments

• Capture.PNG
21.4 KB · Views: 3,562
I go this though for the B part of this problem which was conflicting with part C. This is the correct answer

#### Attachments

• Capture1.PNG
19 KB · Views: 2,855

## What is potential energy of a spring?

Potential energy of a spring is the energy stored in a compressed or stretched spring due to its position or deformation.

## What factors affect the potential energy of a spring?

The potential energy of a spring is affected by the spring constant, which is a measure of its stiffness, and the displacement or compression of the spring from its equilibrium position.

## What is the formula for calculating potential energy of a spring?

The formula for potential energy of a spring is PE = 1/2 * k * x^2, where PE is potential energy, k is the spring constant, and x is the displacement of the spring.

## What is the unit of measurement for potential energy of a spring?

The unit of measurement for potential energy of a spring is joules (J).

## What is the relationship between potential energy and kinetic energy of a spring?

Potential energy and kinetic energy of a spring are interrelated, as potential energy is converted into kinetic energy when the spring is released from its compressed or stretched position.

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