The Who Must Apply the Larger Force to Sweep?

[msimard8]

The Queston

To people are sweeping the floor using identicle brooms. They each clear off the same area and in the process, do the same amount of total work. One persons holds the handle at 15 degrees above the floor, while the other hodlds the handle at 35 degrees above the floor. Which person must use the laarger force to sweep the floor?

I am not quite sure how to attempt this. Ill explain some of my thought processes

Using the equation w=fdcos0, It tells that the 35 degrees broom has less force.


i figured that the person holding the broom at 35 degrees had to apply a less force because they are pulling the broom upward which may reduce friction. But how does this account for the gravity pulling the broom down.

If gravity was the factor, wouldn't the person holding the broom 15 degrees above the floor have it easier since they are not pulling against gravity.

I don't think thinking right. help

 

[Eivind]

I think the broom whit 15 degree angle will be the one you have to use the least force on.

 

[mrjeffy321]

In both cases (15 degrees and 35 degrees), some of the force being applied is going stright down into the ground, and some of it is directed parallel to the ground. Normally, Work = Force * distace, but as pointed out, in this case where the force is being applied at an angle to the movement, W = F*d*cos(angle). If we know that bother brooms travell the same distance and do the same work, it comes down to which force is directed more in the direction of movement, which angle has a larger cosine.

cos(35 degrees) = .819
cos(15 degrees) = .966

So we can see that the 15 degree broom needs a smaller force aplied to do the same work as the 35 degree broom.