Question

1. Solve the following problem on a clean sheet of paper. A package of mass 2.00 kg is released on a 58.2° incline, a distance D-2.5 m from a long spring with spring constant k= 150 N/m that is attached to the bottom of the incline, as shown. The coefficient of kinetic friction is 0.200 between the block and the incline. WWWKO- a. Calculate the maximum compression of the spring. b. What is the total work done on the mass when released from rest to max compression of the spring? c. Calculate the work done by gravity during the fall. d. Calculate the work done by the spring during the fall. e. Calculate the work done by friction during the fall.

Answer 1

a) let the compression of the spring is x

Using work energy theorem

work done by gravity + work done by spring + work done by friction = 0

2 * 9.8 * (2.5 + x) * sin(58.2 degree) - 0.50 * 150* x^2 - 0.20 * 2 * 9.8 * (2.5 + x) * cos(58.2 degree) = 0

solving for x

x = 0.801 m

the maximum compression in the spring is 0.801 m

b)

the total work done on the mass is 0 (change in kinetic energy)

c)

work done by gravity = 2 * 9.8 * (2.5 + 0.801) * sin(58.2 degree)

work done by gravity = 55 J

d)

work done by spring = - 0.50 kx^2

work done by spring = -0.50 * 150 * 0.801^2

work done by spring = -48.2 J

e)

work done by friction = - 0.20 * 2 * 9.8 * (2.5 + 0.801) * cos(58.2 degree)

work done by friction = -6.8 J

work done by friction is -6.8 J