A 1.7 kg breadbox on a frictionless incline of angle ? = 41 ? is connected, by a

Question

A 1.7 kg breadbox on a frictionless incline of angle ? = 41 ? is connected, by a cord that runs over a pulley, to a light spring of spring constant k = 110 N/m, as shown in the figure. The box is released from rest when the spring is unstretched. Assume that the pulley is massless and frictionless. (a) What is the speed of the box when it has moved 10.1 cm down the incline? (b) How far down the incline from its point of release does the box slide before momentarily stopping, and what are the (c)magnitude and (d) direction of the box's acceleration at the instant the box momentarily stops? Please show all work!! Thanks!

Explanation / Answer

a)

conserving energy between initial and final position

deacrease in potential energy of block = increase in potential energy of spring and kinetic energy of block

mg0.101 sin41 = 0.5 xkx0.101x0.101 + 0.5 m v2

v = 0.7999 m/sec

b)

at lowest point V = 0

there fore we get

mg x sin41 = 0.5kx2

x = 0.1989 m

c)

NEtforce on block = ma

k(0.1989) - mgsin41 = ma

a = 6.429 m/sec^2 ( upward along the incline)

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