How Do Two Friends Balance a 200kg Crate Up Stairs?

[Greenrose]

Hi I am struggling with this physics question can u help please
2 friends are carrying a 200kg crate up a flight of stairs. The crate i 1.25m long and 0.50m 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 slpoe of stairs. If the force of each person is vertical, what is the magnitude of each force?

 

[Astronuc]

The center of mass is at the center, however, when the crate is rotated 45°, the rotation of the crate shifts the CM over the person on the back edge.

On a level ground, assuming CM was in the center, then both people would support half the weight.

Draw a picture of a rectangle rotated 45° and determined how much of the area is to the either side of the lower corner, and how that area relates to the shift in CM.

Both people still must support the 200 kg (1960 N), but one will support more than the other.

 

[quicknote]

Hello! It sounds like you are dealing with a situation where forces are in equilibrium. This means that all forces acting on the crate are balanced and there is no net force causing it to move. In this case, we can use the principle of moments to solve for the magnitude of each force.

First, let's draw a free body diagram to visualize the forces acting on the crate. We have the weight of the crate, which is 200kg, acting downwards at its center of gravity. We also have the two forces from the two people carrying the crate, acting upwards at an angle of 45 degrees. Since we know that the crate is not moving, we can say that the sum of the clockwise moments is equal to the sum of the counterclockwise moments.

Now, let's consider the moments caused by the weight of the crate. The weight of the crate is acting downwards at its center of gravity, which is at the center of the crate. This means that the moment caused by the weight is zero, since the distance from the center of gravity to the pivot point (the point where the crate is being carried) is zero.

Next, let's consider the moments caused by the two people carrying the crate. Since we are given that the crate is at a 45 degree angle and the stairs are also at a 45 degree angle, we can say that the distance from the pivot point to the point of application of each force is equal to the length of the crate (1.25m). This means that the moment caused by each person's force is equal to the magnitude of their force multiplied by 1.25m.

Now, since the crate is in equilibrium, we can set the sum of the clockwise moments equal to the sum of the counterclockwise moments. This gives us the equation:

F1 x 1.25m + F2 x 1.25m = 0

Where F1 and F2 are the magnitudes of the forces from the two people carrying the crate. Solving for F1 and F2, we get:

F1 = -F2

Since both forces are acting upwards, we can say that their magnitudes are equal. Therefore, each person is exerting a force of 100kg (200kg/2) to carry the crate up the stairs.

I hope this explanation helps you understand the concept of forces in equilibrium and how to solve for the magnitude of each force. Keep up