A force Fx acts on a particle that has a mass of 1.6 kg. The force is related to

Question

A force Fx acts on a particle that has a mass of 1.6 kg. The force is related to the position x of the particle by the formula Fx = Cx3, where C = 0.5 if x is in meters and Fx is in Newtons. What are the SI units of C? (Use N for Newtons and m for meters) Find the work W done by this force as the particle moves from x = 3.5 m to x = 2.0 m. At x= 2.0 m the force points opposite the direction of the particle's velocity (speed is 12 m/s). What is its speed at 3.5 m? Can you tell its direction of motion at x=3.5 m using only the work-kinetic energy theorem? yes no Explain.

Explanation / Answer

SI unit of C is = SI unit of Fx / SI unit of x^ 3                     = N / m^ 3 (b). work done W = integral F dx with in the intervalsx= 3.5 m to x = 2 m                              = C x^ 3 with in the intervals x= 3.5 m to x = 2 m                              = 0.5 x ^ 3 with in the intervals x= 3.5 m to x = 2 m                              = 0.5 [ x^ 4 / 4 ]   with in the intervals x= 3.5 m to x= 2 m                              = 0.125 x^ 4 with in the intervals x= 3.5 m to x = 2 m                              = 0.125 [ 2^ 4 -3.5 ^ 4 ]                              = -16.75 J (c). velocity v = 12 m / s we know work done W = change in kinetic energy = (1/ 2) m[ V ^ 2 - v ^ 2 ] from this you find V value i..e, speed atx 3.5 m

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