What is the change in kinetic energy of the cart during the move

[gaobo9109]

Homework Statement

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

Homework Equations

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

 

[Hootenanny]

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

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

 

[gaobo9109]

why draw force diagram? There is only one force involved

 

[Hootenanny]

why draw force diagram? There is only one force involved

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.

 

[gaobo9109]

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

 

[Hootenanny]

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

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