Moments Problem -- 2 friends carrying a crate up a flight of stairs

[RyanUSF]

Two friends are carrying a 200kg crate up a flight of stairs. The crate is 1.25m long and 0.500m high and its center of gravity is at its center. The stairs make a 45 degree angle with respect to the floor. The crate is also at a 45 degree angle so the bottom side of crate is parallel to the slope of stairs. If the force of each person is vertical, what is the magnitude of each force?∑Fy = F1 + F2 - m*g = 0The attached picture is my attempt at the solution however the two forces I get are wrong. The bottom force according to my physics textbook is 590N and the top force is 1370N. If someone could tell me where in my solution I mess up it would be much appreciated!

 

[SteamKing]

When you wrote your moment equation to calculate the unknown lifting force, you assumed that the box was horizontal, which gave you a moment arm for the forward force of 1.25 m relative to the rear of the box. This is incorrect. The box is being carried up the stairs such that it makes an angle of 45 degrees with the horizontal (the same angle the stairs make). You have to calculate the moment arms for the moment equation accordingly.

 

[RyanUSF]

When you wrote your moment equation to calculate the unknown lifting force, you assumed that the box was horizontal, which gave you a moment arm for the forward force of 1.25 m relative to the rear of the box. This is incorrect. The box is being carried up the stairs such that it makes an angle of 45 degrees with the horizontal (the same angle the stairs make). You have to calculate the moment arms for the moment equation accordingly.

Since the box is parallel to the stairs though I thought I could assume the box was horizontal. How would I implement the 45 degrees into my calculation of the moment?

 

[SteamKing]

Well, you could make a sketch like you did in the first part of your posted solution, to find the location of the center of the box.

 

[RyanUSF]

Didn't I include the 45° though when I found the total angle from the horizontal (45°) and the moment angle (21.8°) which was 66.8°?

 

[SteamKing]

Yeah, but if you sketch the box canted at a 45 degree angle and locate the forces applied by the two guys carrying the box, you'll see that the distances between the ends of the box and the center are shortened when measured relative to the horizontal. Since the weight of the box is normal to the horizontal, and the support forces are applied vertically according to the OP, it should be readily apparent that the moment arms must be measured parallel to the horizon as well.

IOW, the 1.25 m length of the box is true only when you measure the length of the box at an angle of 45 degrees to the horizontal.