Work — Question 7

Question 7

Holding a load does not require mechanical work on that load

For a constant force, use $W=\vec F\cdot\Delta\vec r$. A person holds a motionless crate with an upward force of 100 N for 30 s. In a second interval the same constant upward force acts while the crate moves 2 m horizontally at fixed height.

1. Find the work of the upward force during the hold.

2. Find its work during the horizontal displacement.

3. Do these results establish that the person uses no stored chemical energy? Explain the missing distinction.

Question 7 - Solution

Holding a load does not require mechanical work on that load

(a) Use displacement, not elapsed time.

The governing relation is $$\boxed{W=\int\vec F\cdot d\vec r,\qquad d\vec r=0\Longrightarrow W=0}$$ The crate displacement is zero during the hold, so $$W=0.$$ Force multiplied by time is not work.

(b) Use the angle.

The upward force is perpendicular to the horizontal displacement: $$W=100(2)\cos90^\circ=0.$$

(c) Keep mechanical recipient and body processes separate.

No. Internal physiological processes and thermal transfers in the person are outside this calculation. Zero mechanical work by one force on the crate does not imply zero energy conversion inside the person.