A spring with k = 15,000N/m is placed on a 30 o incline and compressed someamoun

Question

1. A spring with k = 15,000N/m is placed on a 30o incline and compressed someamount from its equilibrium position. A 5.0 kg block is thenplaced against the spring and released from rest. It isrequired that the block slide exactly 50 cm up the incline from itsinitial position against the compressed spring before momentarilycoming to rest. The coefficient of kinetic friction betweenthe block and the incline is 0.1.

1. (10 points) How far fromthe equilibrium position should the spring becompressed?
2. (10 points) If insteadyou made a mistake and compressed the spring 15 cm from itsequilibrium position, how fast would the block be traveling when itpassed the 50 cm point up the incline?

Explanation / Answer

k = 15,000 N/m, = 30o, m =5.0 kg, d = 50 cm, = 0.1. How far from the equilibriumposition should the spring be compressed? kx2/2 = mgdsin +mgdcos   (1) x = 0.0438 m If instead you made a mistake and compressed the spring 15 cm fromits equilibrium position, how fast would the block be travelingwhen it passed the 50 cm point up theincline?   x' = 15 cm kx'2/2 =mgdsin + mgdcos +mv2/2   (2) (2) - (1) k(x'2 - x2)/2 = mv2/2 v = [k(x'2 - x2)/m] = 7.86m/s

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