Find speed of block on a ramp/pulley
A 20kg block (m1) slides on a 40 degree frictionless ramp. This block is connected to a 30kg block (m2) by a string that passes over a frictionless pulley. The 30kg block is 20cm above the floor and connected to a spring of negligible mass with spring constant 250N/m. The spring is initially unstretched and connected to the floor. The 20kg block is pulled a distance of 20cm down the ramp (so that the 30kg block is 40cm above the floor) and is released from rest. Calculate the speed of each block when the 30kg block is again 20cm above the floor (spring unstretched).
My attempt:
I assumed that you had to use conservation of energy to find v:
Usi + Ugi +KEi = Usf + Ugf + KEf,
where Us is Spring potential, Ug is gravitational potential and KE is kinetic energy.
KE is initially zero so we have
0.5k(xi)^2 + mghi = 0.5k(xf)^2 + mghf + 0.5mv^2
xi is 0.2m, xf is 0.4m for block 2.
I worked everything out and got 10v^2 = 64...which I'm pretty sure is incorrect. Can anyone guide me to the right direction??
Thanks!!
