Math Is Fun Forum

ninjaman

Member

Registered: 2013-10-15

Posts: 61

kinetic energy

hello

I have these two questions

c)    Plot a graph of the kinetic energy of the mass against time. Explain your calculations and state formulae used.

d)    Plot a graph of the kinetic energy of the mass against distance. Explain your calculations and state formulae used.

I have used this formula for the first one,
Ek = ½ mv2 = ½ ma2t2         
Ek is proportional to t2.

this for the second
Ek = ½ mv2 , but we can substitute, giving
Ek = mgy

in not too sure how to show the graphs, but is the above formula along the right lines?
also I have to explain the use of the formula. I think this is just explain why I used it and any transposing required. if anyone knows a better answer for this one please give some advice.

taken from here, http://colourpoint.co.uk/sample_files/physics_as.pdf

this is the first part of the question,

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:

a)    Calculate the total energy expended in the acceleration, I got 11.81 acceleration

b)    Calculate the coefficient of kinetic friction between the mass and the surface.  Suggest materials from which the block and table might be made in order to give such results.  I got 0.155

thanks
simon

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: kinetic energy

c)    Plot a graph of the kinetic energy of the mass against time. Explain your calculations and state formulae used.

Mass against time? Is mass changing with time? Why?

---

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

ninjaman

Member

Registered: 2013-10-15

Posts: 61

Re: kinetic energy

I don't know, the question was given like that. the mass stays the same I imagine. I just think it may have been left in as a clue to finding the answer.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,608

Re: kinetic energy

hi Simon,

it's the KE against time not the mass, so the question does make sense.  As the object speeds up it gains KE so you can plot that against time.

I like to 'assemble' all the known facts like this:

initial velocity = u = 0
final velocity = v = to be determined
time taken = t = 0.92 s
distance travelled = s = 5 m
acceleration = a = to be determined
effective force = applied force less force due to friction = to be determined.
normal reaction of surface = R = mg

Firstly to find v

So that answer is correct. 

On a velocity / time graph, the velocity line is straight, going through the origin so

So

So you'll get a quadratic graph going through (0,0)

Now for the friction:

KE against distance ?

In this case u = 0 so

Hope that helps, 

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

ninjaman

Member

Registered: 2013-10-15

Posts: 61

Re: kinetic energy

thanks for that answer but im terrible with math.
the graph that the tutor showed me looked like a regular graph not a quadratic.
thank you for your help

all the best
simon

Bob

Administrator

Registered: 2010-06-20

Posts: 10,608

Re: kinetic energy

hi Simon,

What do you mean by a 'regular' graph ?  Do you mean a straight line ?

ShivamS has shown how to calculate the work done.  KE and work done are both measured in joules, but, in this question, they are not the same because some of the work is used to overcome friction and so the KE of the mass is less.  Which were you asked for ?

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: kinetic energy

I deleted the older post to put all of the part solutions.
This is about the 10th time I am doing this question from other forums. Let me guess: you go to Teeside university.

a)
Work=force ×distance
W=80 ×5
W=400J

b) Use sigma F = ma. From this find the sum of forces. There are two forces acting: the 80N push and the resisting force of friction. So force of friction = pushing force - ma.

c) Calculate the mass's acceleration from the data that it moves 5 m in 0.92 seconds: from  d = 1/2 at^2 and solve for a. Then calculate velocity as a function of time:   v = at. Finally Kinetic Energy as a function of time is  KE= 1/2mv^2 = 1/2m(at)^2

d) Kinetic Energy as a function of distance is  v^2 = 2ad so  Kinetic Energy = 1/2mv^2 = 1/2m(2ad)

ninjaman

Member

Registered: 2013-10-15

Posts: 61

Re: kinetic energy

hello

sorry I didn't realize shivams had posted something. I go to a college in Hampshire, not teeside.
please could you point out the other forum or thread as I don't want to have to post the same thing if its already been answered with advice
thanks
simon

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: kinetic energy

I don't have the links but what I wrote in my last post it really all the advice you will get from the other forums.

Are we done with the problem or is there something else you don't understand?