A force Fx acts on a particle that has a mass of 1.5 kg. The forceis related to

Question

A force Fx acts on a particle that has a mass of 1.5 kg. The forceis related to the position x of the particle by the formula Fx =Cx^3 where C = 0.50 if x is in meters and Fx is in newtons.
a) what are the SI units of C?
b)Find the work done by this force as the particle moves from x =3.0 m to x = 1.5 m
c)at x = 3.0 m, the force points opposite the direction of theparticle's velocity (speed is 12.0 m/s)
What is its speed at x = 1.5 m? Can you tell its direction ofmotion at x =1.5 m using only the work-kinetic energy theorem?Explain

Explanation / Answer

a) The units of C = Fx / x3 so units are N / m3 b) W = int { Fx.dx}           = [C *x4 / 4 ] 1.53.0 = 0.5 [ 20.25 - 1.2656] = 9.492 J c) W = 0.5m [v22 -v12]    = 0.5 * 1.5 [ 144 -v12] ==>   v1 = 11.46 m/s

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