A uniform rectangular crate of mass 150 kg is 6 m tall and 2.20 m wide. It's coefficient of friction with the floor is .7

What minimum horizontal force is needed to slide this crate along the floor at constant speed?

How high up on the crate can this force be applied without tipping over the crate?

Question

A uniform rectangular crate of mass 150 kg is 6 m tall and 2.20 m wide. It's coefficient of friction with the floor is .7

What minimum horizontal force is needed to slide this crate along the floor at constant speed?

How high up on the crate can this force be applied without tipping over the crate?

aaronq · Answer

At constant speed means that there is no acceleration, the friction and force being put upon it forward are balanced  

 $\sum F_x(net)=F_{push}+f=ma=0$

Sub in:   $f=\mu N$

$\sum F_x(net)=F_{push}-\mu N=0$

Find the normal force with the forces in the y-direction.

$\sum F_y(net)=N+F_g=0\rightarrow N=-F_g=-(-mg)=mg$

Thus: $F_{push}-\mu mg=0 \rightarrow F_{push}=\mu mg $