Understanding the Chain Rule in Mechanics: Solving for Acceleration and Force

[AshesToFeonix]

Homework Statement

6. A particle of mass m moves along a frictionless, horizontal plane with a speed given by

v(x) = α / x. Where x is the distance of the object from the origin and α is a constant.

Working with F = ma, we want to get the acceleration. You have v = v(x). You want a = dv/dt. Find (dv/dx)(dx/dt). Find the force F(x) to which the particle is subjected to.

The Attempt at a Solution

I guess my problem is I don't understand why I need to use chain rule since v = dx/dt. I thought I could take the derivative in respect to t on both sides, and get dv/dt = - α / x^2, then multiply both sides by m to get the force equation.

the answer is given, -m α^2/ x^3. So can someone explain what I'm missing here...

 

[Kurdt]

You need to use the chain rule because x is some function of t. What you have done above is find dv/dx. Now you have correctly identified dx/dt as v and you know v = a/x, so what is (dv/dx)*(dx/dt)?

 

[AshesToFeonix]

wow awesome thanks that clears up a lot. I almost gave up on anyone answering me. I read that there was a way to close a thread or say that the problem is solved but I'm not seeing it on here so I guess'll have to leave it as is.

 

[Kurdt]

The forum software was upgraded recently and I think only mentors can mark it solved at the minute. Just leave it as it is for now.