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Answers
A force F = 20 + 10y acts on a particle in y direction where F is newton and y is metre. Find Work Done by this force to move the particle from y = 0 to y = 1m.
a) 30 J
b) 5 J
c) 25 J
d) 20 J
- Force acting on the object,F = 20 + 10y
- Displacement from y = 0 to 1 m
To find
Work Done by the force in displacing the object
Since,
The force acting on the object is a variable force,we need to integrate the given function with respect to 'y'.
We Know that,
On integrating F w.r.t to y,we get :
REFER TO THE ATTACHMENT
Thus,the work done by the force is 25 J___________(Option C)
- Force is given as F = 20 + 10y.
- Displacement of particle from y = 0 to y = 1m.
As The Force is Changing w.r.t Displacement,
Therefore,
The applied Formula Should be,
As the Body is moving towards y - axis.
The Formula becomes,
Substituting the values,
Applying the limits,
Now, Integrating,
The above integration Formula used is :-
Now, Simplifying the equation,
Substituting the value of y values,
So, the work done by the force is 25 Joules .