Acceleration as a Function of Distance

[bollocks748]

Homework Statement

Consider a block of mass M that is pulled up an incline by a force T that is parallel to the surface of the incline. The block starts from rest and is pulled a distance x by the force T. The incline, which is frictionless, makes an angle theta with respect to the horizontal.

1.1 Write down the work done by the force T.


1.2 Calculate the potential energy of the block as a function of the position x. From the work and the potential energy calculate the kinetic energy of the block as a function of position x.


1.3 Calculate the acceleration, a, of the block as a function of position x. Calculate the velocity of the block from the acceleration and hence the kinetic energy as a function of position. Show that the kinetic energies calculated in these two ways are equivalent.


1.4 Calculate the ratio of the potential to kinetic energy. What happens to this ratio for large T? Check your answer for the case theta = pi/2 which you should be able to recalculate easily.

Homework Equations

I didn't have problems with the first two parts, but I might as well put them here just in case:

Work done by T = T*x

PE(x)= m*g*x*sin(theta)

The Attempt at a Solution

What I'm really having trouble with is defining acceleration as a function of x, in part 3. I've had to do it before using the chain rule, but most of the time I was given a function of v(x), and integrated it, or used dv/dx and dx/dt to find dv/dt, or something of that nature. But I've never encountered a problem where I wasn't given some starter formula to work with... and I'm really at a loss here. Please help!

 

[Hootenanny]

What I'm really having trouble with is defining acceleration as a function of x, in part 3. I've had to do it before using the chain rule, but most of the time I was given a function of v(x), and integrated it, or used dv/dx and dx/dt to find dv/dt, or something of that nature. But I've never encountered a problem where I wasn't given some starter formula to work with... and I'm really at a loss here. Please help!

You're on the right lines with use of the chain rule. Note that although you haven't been given an equation explicitly, you can formulate one yourself. Consider applying Newton's Second Law to the block.

Be aware that T is not the only force acting on the block.