Answer:
From highest to lowest: [tex]W_1>W_2>W_3[/tex]
Explanation:
The work done by a force is given by
[tex]W=Fd cos \theta[/tex]
where:
F is the force applied on the object
d is the displacement of the object
[tex]\theta[/tex] is the angle between the direction of the force and of the displacement
In case 1), the barbell is lifted upward. This means that:
- the force applied is upward
- the displacement of the object is upward
This means that [tex]0<\theta<90^{\circ}[/tex], so the work done is positive: [tex]W_1>0[/tex]
In case 2), the barbell is held stationary: this means that the displacement is zero,
[tex]d=0[/tex]
And therefore, this means that the work done is also zero:
[tex]W_2=0[/tex]
In case 3), the barbell is put down slowly, without dropping it. This means that:
- The force applied is still upward (in fact, the force applied must be upward in order to overcome the force of gravity downward, and avoid the barbell to fall down)
- The displacement of the barbell is downward
This means that [tex]90^{\circ}<\theta<180^{\circ}[/tex], so [tex]cos \theta<0[/tex], and therefore the work done is negative:
[tex]W_3<0[/tex]
So the ranking from greatest to smallest work is
[tex]W_1>W_2>W_3[/tex]
