Question

A 200g block slides back and forth on a frictionless surface between two springs, as shown. The left-hand spring has k = 130 N/m and its maximum compression is 16cm. The right-hand spring has k = 280 N/m. Find (a) the maximum compression of the right-hand spring and (b) the speed of the block as it moves between the springs.

Answer 1

energy stored in LH spring at max = (1/2)kx^2 = (1/2)130(.16)^2

same amount will be stored in the RH spring when it is compressed all the way

(1/2)130(.16)^2 = (1/2)280 x^2

x^2 = (130/280).16^2

x = .11 meter = 11 cm

part b
(1/2)k x^2 = (1/2)m v^2
130 * .16^2 = .2 v^2

v = 4..08 m/s

Answer 2

By the way, I answered your roller question problem long ago.