- #1
patrykh18
- 32
- 2
Homework Statement
A string is attached to a block that can slide along a frictionless horizontal surface aligned along the x axis. The left end of the string is pulled over a pulley of negligible mass and friction at a height of 1.3m so that the block slides from x1=3m to x2=1m. The tension in the string remains constant (25N). Calculate the ∆KE.
Homework Equations
W=F•x=|F||x|cosA where A is the angle
KE=0.5mv^2
∆KE= KE final- KE initial
The Attempt at a Solution
In my first attempt I got an answer of 30.49 J. What I did is I I said that ma=-25cosA so a=-(25cosA)/m
I integrated with respect to t. Since the velocity at x=3m is not stated I let it equal v0. So the integration constant was v0. I integrated v with respect to time. My integration constant was 3 as that was the original displacement. Next I found the time at which x=1m in terms of m (I knew the angle at that time using basic trigonometry). I took my value of time and plugged it back into equation for velocity.
After doing it I realized that obviously my answer is wrong as I treated cosA like a constant as I was intergrating. My problem is that i can't figure out the expression for A as a function of time.
I have attached below a diagram of the system. Any help will be much appreciated.