A 5 kg block is placed near the top of a frictionless ramp, which makes an angle of 30o degrees to the horizontal. A distance d = 1.3 m away from the block is an unstretched spring with k = 3000 N/m. The block slides down the ramp and compresses the spring. Find the magnitude of the maximum compression of the spring.

Question

xmax=?

Answer 1

Use conservation of energy.
At the top of the ramp and end of compression, the kinetic energy is zero, so
Initial gravity P.E. = Final spring P.E.

M g d sin30 = (1/2) k Xmax^2

Solve for Xmax

Answer 2

.146

Answer 3

0.15419320656221194

Answer 4

.145679

Answer 5

you must account for the distance the spring compresses as well as the 1.3m the block travels the final equation will turn out to be a quadratic