To move a large crate across a rough floor, you push on it with a force F at an

Question

To move a large crate across a rough floor, you push on it with a force F at an angle of 21 ? below the horizontal, as shown in the figure.
A) Find the force necessary to start the crate moving, given that the mass of the crate is 32 kg and the coefficient of static friction between the crate and the floor is 0.54.

To move a large crate across a rough floor, you push on it with a force F at an angle of 21 ? below the horizontal, as shown in the figure. A) Find the force necessary to start the crate moving, given that the mass of the crate is 32 kg and the coefficient of static friction between the crate and the floor is 0.54.

Explanation / Answer

For the sum along y,

N - Fsin21 - mg = 0

--> N = mg + Fsin21

For the sum along x,

Fcos21 - ukN = 0

Using our expression for N,

Fcos21 - uk(mg + Fsin21) = 0

Solving for F by plugging in our given values,

F = 229 N [ANSWER]

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