How Do You Graph Kinetic Energy Against Time and Distance?

[james123]

<Moderator's note: Moved from a technical forum and thus no template.>

A horizontal force of 80 N acts on a mass of 6 kg resting on a horizontal surface. The mass is initially at rest and covers a distance of 5 m in 0.92 s under the action of the force. Assuming there are no energy losses due to air resistance and therefore that the acceleration is constant:

1. (a) Calculate the total energy expended in the acceleration.
   
   (b) Plot a graph of the kinetic energy of the mass against time.
   
   (c) Plot a graph of the kinetic energy of the mass against distance. Work done so far:
   
   1. (a) 80 x 5= 400J
   
   1 (b) a= 2d/t^2
   a=(2x5)/0.92^2
   a=11.8147448
   a=11.81 m/s^-2
   
   v=at
   v=11.8147448 x 0.932
   v=10.86956522
   
   KE=1/2m(at)2
   KE=0.5 x 6(10.86956522)^2
   KE=354.4423442 J
   
   1 (c) KE=1/2m(2ad)
   KE=0.5 x 6(2 x 11.8147448 x 5
   KE=354.442344 JMy main questions are, should I expect the same answers for both questions? seems a little odd to me.
   Also, I'm completely stumped on the graphs, how to start them, how to plot them etc.
   
   Any help is greatly appreciated!
   

 

[BvU]

should I expect the same answers for both questions? seems a little odd to me.

Why ? There is only one kinetic energy at t = 0.92 s, which is what you calculated in b) and c). What the exercise asks is a plot of KE vs t in b) and vs d in c). So far you have two points (t=0 and t = 0.92 s) for the first and two points (d=0 and d=5 m) for part c).

Please post in the homework section and use the template

Oh, and if the exercise given data are in two digits, don't report in 10 digits (calculating in that many digits is just fine though, with todays equipment ).

 

[james123]

Hi, thanks for replying.

I have now posted in the homework section.

I think I was just suspicious about getting two of the same answers, I assumed I was doing something wrong.

After thinking about it, it now makes sense, just got to figure out these graphs!

 

[james123]

My first graph for 1(b) has ended up looking like this, is this along the right lines??

 

[BvU]

Does it look like a graph of

KE=1/2m(at)² ?

And: does it show

KE=354 J

at t = 0.92 s ?

 

[james123]

Sorry, the graph I posted was generic and isn't mine, just used it as an example to show the general shape of what I ended up with.

That said, I've re-done the graphs and think I have it. Please ignore the values as again these aren't my graphs.

For question 1 (b) I have this graph where KE grows exponentially.

And for 1(c) I have needed up with a straight line graph

Still trying to figure out how to upload my own pictures from a MacBook! Are these the shaped of graph I should expect??

Thanks for chipping in so far, I really appreciate it

 

[BvU]

Are these the shaped of graph I should expect?

Yes. a parabola for KE=1/2m(at)² and a straight line for KE=1/2m(at)2