Respuesta :
Answer:
Workdone = 5 units
Step-by-step 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.
[tex]W = \int\limits^a_b {F} . ds[/tex]
- 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:
[tex]W = \int\limits^a_b {(-3x^2i - 4xj}) . (1 i -3j)\\\\W = \int\limits^a_b {(-3x^2 + 12x}).dx\\\\W = -x^3 + 6x^2 |^1_0\\\\W = -1 + 6 = 5[/tex]
