The magnitude of a certain one-dimensional force varies according to: F = 9.6x -
ID: 2177816 • Letter: T
Question
The magnitude of a certain one-dimensional force varies according to:F = 9.6x - 0.531x3
where x is the displacement from the origin in meters, and F is the magnitude of the force in Newtons. At t = 0, a mass m = 222 g is at the origin moving in the positive x-direction at speed v = 8.58 m/s when this force begins to act on it.
ASSUME: there are no other forces acting on the mass.
a) Find the work done by the force on the mass when it reaches x = 1.57 m?
J
b) Find v, the speed of the mass when it reaches x = 1.57 m?
m/s
Explanation / Answer
Work = integral(Fds)
= integral(9.6x - 0.531x3)ds {from 0 to 1.57}
= 11.02J
b) Work done = change in kinetic energy
11.02 = 0.5*0.222*(v2 - 8.582)
v = 13.11m/s
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