# Does a man do work when he carries a 75 N bag horizontally for 5 m? Why / why not?

Jan 17, 2018

No, he does not perform work.

#### Explanation:

The work is the product of the force that is in the direction of the displacement. The formula for work uses the vector dot product to properly handle a situation in which the force and displacement are not parallel.

Let the force be F, the displacement be D, and the angle between F&D be $\theta$. Therefore, the formula is

$\text{Work} = F \cdot D$

Expanding the formula to show the cosine term from the dot product,

$\text{Work} = F . D . \cos \theta$

Our data is that ...
F=75N
D=5 m
$\theta = {90}^{\circ}$

Solve..

$\text{Work} = 75 N . 5 m . \cos {90}^{\circ} = 0$

So he does not do work. Not in the Physics sense.

Hope this helped you!

Jan 19, 2018

$\text{please watch the animations below.}$

#### Explanation:

• In which situations does the force work?

• The force does the work because the direction of force is the same as the direction of displacement.

• The force does the work because the direction of force is opposite to the direction of displacement.

• The force can not do the work because the force is perpendicular to the direction of displacement.

• The force can not do the work because the force is perpendicular to the direction of displacement.

• The blue component does the work but the green component can not do the work.

• The solution to your problem is: the weight of the bag is down, the force you use to lift is upward, and the displacement is horizontal (conforms to the 3rd and 4th angles). work is not done.