Problem 8 – 19P*: A 2.00 kg block is placed against a springon a frictionless 30
ID: 1662432 • Letter: P
Question
Problem 8 – 19P*: A 2.00 kg block is placed against a springon a frictionless 30.0° incline (see figure). (The block is notattached to the spring.) The spring, whose spring constant k is19.6 N/cm, is compressed 20.0 cm and then released. (a) What is theelastic potential energy of the compressed spring? (b) What is thechange in the gravitational potential energy of theblock–Earth system as the block moves from the release pointto its highest point on the incline? (c) How far along the inclineis the highest point from the release point?
Explanation / Answer
m=2kg; =30; k=19.6N/m; x=0.2m; a)the elastic potential energy of the compressed spring is1/2kx2=1/2*19.6*.22=0.392J; b) according to conservation of energy loss in elastic potentialenergy = change in thegravitational potential energy of the block–Earth system; so PE=0.392J; c) mgh=0.392; mgLsin30=0.392; L=0.392/2/9.81*2=0.039m.