F = MA 2012 Exam # 19, 20 (Using Graphs)

[SignaturePF]

Woops, it's the 2010 exam -- my bad.

Homework Statement

They have diagrams that I'm not sure how to display; so find them at the following link:
https://aapt.org/physicsteam/2010/upload/2010_Fma.pdf
These are #'s 19 and 20 and they refer to the PE graph in 18.

Homework Equations

Not sure, perhaps:
E_mec = K + U

The Attempt at a Solution

I'm not at all sure how to use the PE graph and a position vs time graph to find total energy or describe the motion. Also, I'm not sure how a potential energy vs position could give rise to position vs time. If anyone could direct me to the concept or link that I'm missing -- that'd be great.

 

[Simon Bridge]

Use the graphs separately.
What is the motion of the particle in the potential?
(You did Q18 OK didn't you? So you know the forces?)

i.e. Will the particle have a constant velocity or just hold it's position, or accelerate or what?

Then look at the position time-graphs. What kind of motion do each describe?
Which one matches up?

You can do it the other way around ... look at the first graph: what is the particle doing? What happens to it's position?
Now look at the potential vs position graph - does that make sense? (This is probably easier.)

For Q20 - it is pretty much the same ... what is the motion of the particle? Describe it in words - is it sitting still, moving at a constant velocity, oscillating between limits, what? At what kinetic energy would the particle have t have in order to have that motion?

 

[SignaturePF]

So for numeral I, it makes sense since net force is 0 at 15m so acceleration is zero and this can be represented by a constant position. TRUE
For numeral II, there should be a positive acceleration but the position vs time graph is constant; clearly FALSE.
Numeral III, the velocity is constant - thus the acceleration is zero. This agrees with the graph. TRUE
So 19 is both I and III. Thanks

Here's a thought for 20:
E_mec = K + U
E_mec = 1/2mv^2 + U
Let's make it easy on ourselves by finding where v = 0 (where dx/dt = slope = 0)
Two points of this are: x = 5 m and x = -5m
Here K = 0 so
E_mec = U
Tracking these points on the graph both yield:
-5J

Wow, those questions were actually kind of easy; thanks for your insight. I guess I should really pay more attention to what I am given.

 

[Simon Bridge]

Reading graphs is a skill that many people resist learning because it looks harder than it is. It is actually a good shortcut to solutions.

i.e. #20 the graph shows the particle oscillating sinusoidally between -5 and +5 ... to find the kinetic energy that does that, draw a horizontal line through the potential energy graph and see where it intersects.

All the difficult part is in knowing which lines to draw.
Anyway - well done.

 

[Nickie]

Hello,

Thank you for providing the link to the diagrams. I can see that the problem involves a mass on a spring system, with a position vs time graph and a potential energy vs position graph. To use these graphs to find total energy or describe the motion, we can use the following equations:

1. Total Energy (E) = Kinetic Energy (K) + Potential Energy (U)
2. Kinetic Energy (K) = 1/2 * mass * velocity^2
3. Potential Energy (U) = 1/2 * spring constant * displacement^2

From the position vs time graph, we can determine the velocity of the mass at any given time by calculating the slope of the curve at that point. This velocity can then be used to calculate the kinetic energy.

From the potential energy vs position graph, we can determine the displacement of the mass at any given position. This displacement can then be used to calculate the potential energy.

By using these equations and the information from the graphs, we can determine the total energy of the system at any given time and describe the motion of the mass.

I hope this helps and please let me know if you have any further questions. Thank you.