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

In summary, the conversation discusses the use of the chain rule to determine the net force acting on an object with a mass of 1500kg, given its movement function v(x)=(4.0 [1/ms]) * x^2. The correct solution involves finding the first order derivative of v(x) and multiplying it by v(x) to get F(x)=m*v(x)*v'(x). The final answer is F(x)=1500[kg]*32.0[1/m^2*s^2]*x^3. The person asking for confirmation is advised that their solution is correct.
  • #1
mg11
14
0

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.
 
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  • #2
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?
 
  • #3
rock.freak667 said:
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!
 
  • #4
mg11 said:
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).
 
  • #5
rock.freak667 said:
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?
 
  • #6
I have an exam tomorrow that includes a question of this type. Could someone please just confirm if I'm right?

Thanks
 
  • #7
What did you use for dv/dx ?
 
  • #8
SammyS said:
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)
 
  • #9
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.
 
  • #10
Yes, it looks fine !
 
  • #11
SammyS said:
Yes, it looks fine !

Great, Thank you!
 

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

1. What is the chain rule and how does it apply to finding F(x) when v(x) is given?

The chain rule is a mathematical tool used to find the derivative of a composite function. In other words, it allows us to find the rate of change of a function that is made up of multiple functions. When finding F(x) with v(x) given, the chain rule helps us determine the derivative of v(x) with respect to x, which is needed to find F(x).

2. Can you provide an example of using the chain rule to find F(x) when v(x) is given?

Yes, for example, if v(x) = sin(x^2), we can use the chain rule to find F(x) by first finding v'(x) = 2xcos(x^2). Then, F(x) = ∫v'(x)dx = ∫2xcos(x^2)dx = sin(x^2) + C.

3. What are the steps for using the chain rule to find F(x) when v(x) is given?

The steps for using the chain rule to find F(x) when v(x) is given are as follows:
1. Identify the inner function, u, and the outer function, v.
2. Find the derivative of the outer function, v'(x).
3. Replace the inner function, u, with its derivative, u'(x).
4. Multiply the outer and inner derivatives, v'(x) * u'(x).
5. Integrate the result to find F(x).

4. What is the importance of using the chain rule when finding F(x) with v(x) given?

The chain rule is important because it allows us to find the derivative of a composite function, which is necessary for finding F(x) when v(x) is given. Without using the chain rule, it would be difficult to find the derivative of v(x) and thus, difficult to find F(x).

5. Are there any common mistakes to avoid when using the chain rule to find F(x) with v(x) given?

Yes, some common mistakes to avoid when using the chain rule include forgetting to multiply the outer and inner derivatives, using the wrong derivative for the inner function, and not simplifying the result before integrating. It is important to carefully follow the steps and check your work to avoid errors.

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