Find F(x) when v(x) is given. Chain rule?

[mg11]

Homework Statement

The movement of an object with a mass of 1500kg is given by v(x)=(4.0 [1/ms]) * x^2

Determine the net force acting on the object as a function of x.

Homework Equations

F=ma

The Attempt at a Solution

I know I'm supposed to use the chain rule to solve this but I have no idea how I'm supposed to do it. My instinct is to just find the 1st order derivative of this equation to get a(x) and then according to Newton's second law F(x)=m*a(x) will give me the final answer. But since I am told to use the chain rule, I suspect that it might be incorrect to simply differentiate v(x) as is.

An explanation would be great, but if I can even just get the correct final answer I would be able to try and make sense of it myself.

Thank you.

 

[rock.freak667]

You can get dv/dx, but you know that a = dv/dt by definition.

You can rewrite it as dv/dt = dv/dx * dx/dt

and dx/dt is the same as?

 

[mg11]

You can get dv/dx, but you know that a = dv/dt by definition.

You can rewrite it as dv/dt = dv/dx * dx/dt

and dx/dt is the same as?

dx/dt is the same as v(t) but I don't know v(t), or do I?

Thanks!

 

[rock.freak667]

dx/dt is the same as v(t) but I don't know v(t), or do I?

Thanks!

Usually it would be v(t), but remember you can re-write it in terms of x to get v(x). So in this case it is simply v(x).

 

[mg11]

Usually it would be v(t), but remember you can re-write it in terms of x to get v(x). So in this case it is simply v(x).

OK, so in that case would the answer be F(x)=m*a(x)=m*v(x)*v`(x) ?

I did this and got F(x)=1500[kg]*32.0[1/m^2*s^2]*x^3

Is that right?

 

[mg11]

I have an exam tomorrow that includes a question of this type. Could someone please just confirm if I'm right?

Thanks

 

[SammyS]

What did you use for dv/dx ?

 

[mg11]

What did you use for dv/dx ?

I differentiated the original function v(x) and got

dv/dx = 2 * 4.0[1/ms] * x

Then I multiplied it by the original v(x) and got

2 * 4.0[1/ms] * X * 4.0[1/ms] * x^2 = 32.0[1/m^2*s^2] * x^3
--------------------- --------------------
dv/dx v(x)

 

[mg11]

Can anyone just give me a yes/no answer to this? Did I solve right?

I have to go to sleep soon before the test tomorrow. I would really appreciate some help.

 

[SammyS]

Yes, it looks fine !

 

[mg11]

Yes, it looks fine !

Great, Thank you!