Cart pulled by cord over pulley: finding change in kinetic energy

[math_head7]

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, or negligible mass and friction and at cord height h = 1.20m, so 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 the kinetic energy of the cart during the move?

Homework Equations

W=F_xcos$$\Theta$$d ?
$$\Delta$$K= 1/2mv2²_F - 1/2mv²_I ?

The Attempt at a Solution

I attempted to find theta by doing tan^-1(1.2/2) getting angle 31.96 degrees. I then plugged that into F_xcos(31.96)d = 25Ncos(31.96)2.00m = 42.9J which was my answer. But the book says it's 41.7J. I just can't figure it out...

 

[tiny-tim]

welcome to pf!

hi math_head7! welcome to pf!

(have a theta: θ and a delta: ∆ and a degree: ° )

i assume the lower end of the string stays 1.2 m below the pulley, so that the angle changes?

you've calculated it as if the angle stays the same

you'll need to integrate (alternatively, there is a trick using conservation)

try again! ​

 

[math_head7]

Thanks tiny-tim.

I didn't consider at all that θ was changing. Thanks to that advice I was able to figure it out.