A1.1 kg block is initially at rest on a horizontal frictionless surface when a horizontal force in the positive direction of an x axis is applied to the block. the force is given by f with arrow(x) = (2.4 − x2)i hat n, where x is in meters and the initial position of the block is x = 0.
(a) what is the kinetic energy of the block as it passes through x = 2.0 m?
(b) what is the maximum kinetic energy of the block between x = 0 and x = 2.0 m?

Answer with Explanation:

Mass of block=1.1 kg

Th force applied on block is given by

F(x)=

Initial position of the block=x=0

Initial velocity of block=

a.We have to find the kinetic energy of the block when it passes through x=2.0 m.

Initial kinetic energy=

Work energy theorem:

Where Final kinetic energy

=Initial kinetic energy

Substitute the values then we get

Because work done=

Hence, the kinetic energy of the block as it passes thorough x=2 m=2.13 J

b.Kinetic energy =

When the kinetic energy is maximum then

Substitute x=

Substitute x=

Hence, the kinetic energy is maximum at x=

Again by work energy theorem , the  maximum kinetic energy of the block between x=0 and x=2.0 m is given by

Hence, the maximum energy of the block between x=0 and x=2 m=2.48 J

and 1and 1

resonant frequency