Question

The only force acting on a 0.5 kg object as it moves along the x axis is given by

        F = (4x i – 3x2y j ) N. where x and y in meter. The object starts moving with

        velocity of 4 m/s.

a) Find the work done by the force as the object moves from x = 1 to x = 3m.

 b) What is the speed of the object at x = 3 m?

please solve a & b

Answer 1

Given, mass of the object (m) = 0.5 kg

force acting on the object (F) =

initial velocity of the object (u) = 4 m/s

(a) Work done by a force in moving a object by S distance in a specified direction (i.e. displacement) is given by

  

....................................(1)

Where, F is the force acting on the object

  

As the object moves only in the x direction (i.e. from x =1 m to x = 3 m) or along the line

'' y = 0 '' .

or, dy = 0

So, the integration (given by equation (1)) will be along the line "y =0" . Then

  

or,

or,

or,   

or.   

This is the work done by the given force as the object moves from x = 1m to x= 3m .

(b) From Newton's second law of motion

or,   

So,    (for the given problem)

or,

Again the only component of acceleration in x direction is

a = 8x

Now, we know that

or,   

or, (As the initial velocity of the object was 4 m/s)

or,

or,

or,   

or,   

or,

This is the speed of object at x = 3m.

For any doubt please comment . Thank you.