Question

a force F is related to position of the particle by the relation F=10x^2 N find the workdone by the force when particle moves from x=2m to x= 4m

Answer 1

F=10x²...
now we know, dU/dx= -F.
so, dU=-10x²dx
=>integrating both sides w.r.t x we have
=>U=10[x^3/3]from limits x=2 to x=4
=>U=-(10×56)/3=-186.6joules .
Hence U=-186.6 joules.