b) An object of mass 40 kg is been acted upon by a force that changes its velocity from 30 km/h to 25 km/h
How much work is done by the force? Is the work done negative or positive?
Answers
Given:-
→ Mass of the body = 40kg
→ Initial velocity of the body = 30km/h
→ Final velocity of the body = 25km/h
To find:-
→ Work done by the force and is it
positive or negative.
Solution:-
Firstly, let's convert the initial and final velocity of the body from km/h to m/s.
=> 1 km/h = 5/18 m/s
=> 30km/h = 5/18×30
=> 8.33 m/s (u)
=> 25km/h = 5/18×25
=> 6.94 m/s (v)
_____________________________
Now, we know that :-
Work done = Change in Kinetic energy
=> W = Final K.E. - Initial K.E.
=> W = 1/2mv² - 1/2mu²
=> W = m/2[v² - u²]
By substituting values, we get :-
=> W = 40/2[(6.94)² - (8.33)²]
=> W = 20[48.1636 - 69.3889]
=> W = 20[-21.2253]
=> W = - 424.506 J
So, we can conclude that as the velocity of the object had decreased with time, hence it was acted upon by a retarding force.
Thus, work done by the force is negative.