Answer:
Workdone = 5 units
Explanation:
Given:-
- The force is defined in cartesian coordinates:
F = xy i + (y-x) j
- Acts for the line between two points:
( 0 , 0 ) & ( 1 , -3 )
Find:-
Find the work done by the force over the straight line.
Solution:-
- The work-done by an force is defined as a dot product of Force (F) and the path at which the force acts (ds) or a path integral of force.
- The path (ds) is defined as straight line between two points. We will determine the equation of line:
y = mx + c
Where, m = ( -3 - 0 ) / ( 1 - 0 ) = -3
c = 0
y = -3x
- We will substitute the value above into Force F:
F = x(-3x) i + (-3x-x) j
F = -3x^2 i - 4x j
- Now evaluate the integral for Work done:
