Question

Mild-mannered Clark Kent pushes a box with a force F at an angle of 21° below the horizontal. Find the force Clark Kent is required to push with to start the crate moving. The mass of the crate is m = 34 kg and the coefficient of static friction between the crate and the floor is 0.67.

N

Answer 1

Given that

The mass of the crate is m = 34 kg

The coefficient of static friction between the crate and the floor is (us) =0.67

Mild-mannered Clark Kent pushes a box with a force F at an angle of 21° below the horizontal.

Find the force Clark Kent is required to push with to start the crate moving.

Now the Fs =usFN

Fs =Fax =Facostheta =Facos(21) =0.933Fa

FN =Fay+mg =Fay+(34)(9.81) =Fasin(20) +333.54 =0.3420Fa+333.54

Now

0.933Fa=  us (0.3420Fa+333.54)

0.933Fa = (0.67) (0.3420Fa+333.54)

0.933Fa = 0.2291Fa+223.47

Fa =233.47/0.704 =331.63N