# Work done by a varying force

1. Apr 27, 2010

### gaobo9109

1. The problem statement, all variables and given/known data
A cord is attached to a cart that can slide along a frictionless horizontal rail aligned along an x-axis. The left end of the cord is pulled over a pulley, located at height h = 1.2m. There is negligible frictional force. The cart slides from x1=3.00m to x2=1.00m. During the move, the tension in the cord is a constant 25.0N. What is the change in kinetic energy of the cart during the move

2. Relevant equations

3. The attempt at a solution
My approach to the question is as follow:
Since tension is constant, the horizontal component of T will decrease as the angle T makes with the horizontal increases. So I need to form an expression for horizontal component of T in term of h and x. But I don't know how to form this equation.

tan

2. Apr 27, 2010

### Hootenanny

Staff Emeritus
HINT: Draw a force diagram and use the properties of a right-angled triangle.

3. Apr 27, 2010

### gaobo9109

why draw force diagram? There is only one force involved

4. Apr 27, 2010

### Hootenanny

Staff Emeritus
Yes, but there is two components and you want the angle between the force and one of its components (in the x-direction). You should then be able to write the angle in terms of the displacement and the pulley height.

5. Apr 27, 2010

### gaobo9109

tanθ = 1.2/x
θ = tan-11.2/x
Tcosθ = Tcos(tan-11.2/x)
Is it like this?

6. Apr 27, 2010

### Hootenanny

Staff Emeritus
It would perhaps be easier to use the fact that
cosθ = x/sqrt(x^2+h^2). Can you see why?