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Ross and Chandler are carrying a 150 kg crate up a flight of stairs. The crate is 2.0 m long and 1.5 m high, and its center of gravity is at its center. The stairs make a 45.0Ā° angle with respect to the floor. The crate also is carried at an 45.0Ā° angle, so that its bottom side is parallel to the slope of the stairs. If the force each person applies is vertical, what is the magnitude of each of these forces

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Answer:

The magnitude of each force is 1309 N and 105 N

Explanation:

The reaction at each lifter due weight and overturning effect (Rā‚, Rā‚‚) is given as:

[tex]R_1=\frac{150}{2} cos(45^0) +\frac{1.5}{2+1.5} *150sin(45^0)=53.03 +45.46=98.49kg\\R_2=\frac{150}{2} cos(45^0) -\frac{1.5}{2+1.5} *150sin(45^0)=53.03-45.46=7.57kg[/tex]

g = 9.8 m/sĀ²

[tex]R_1=98.49*g=98.49*9.8=925.904N\\R_2=7.57*g=7.57*9.8=74.186N[/tex]

Resolving the reactions to the vertical direction, we get:

[tex]R_{1v}=\frac{R_1}{cos(45^0)} =\frac{925.904}{cos(45^0)}=1309N\\ R_{2v}=\frac{R_2}{cos(45^0)} =\frac{74.186}{cos(45^0)}=105N\\[/tex]

The magnitude of each force is 1309 N and 105 N

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