## College Physics (4th Edition)

The normal force is $152.8~N$ The magnitude of the force of static friction exerted on the crate is $88.2~N$ and this force is directed up the ramp at an angle of $30^{\circ}$ to the horizontal.
The normal force $F_N$ is the component of the crate's weight that is directed straight into the surface of the ramp. $F_N = mg~cos~\theta$ $F_N = (18.0~kg)(9.80~m/s^2)~cos~30^{\circ}$ $F_N = 152.8~N$ The normal force is $152.8~N$ Since the crate is not sliding, the force of static friction is exerted on the crate and it is directed up the ramp. Since the speed is constant, the force of static friction $F_f$ exerted on the crate is equal in magnitude to the component of the crate's weight directed down the ramp. $F_f = mg~sin~\theta$ $F_f = (18.0~kg)(9.80~m/s^2)~sin~30^{\circ}$ $F_f = 88.2~N$ The magnitude of the force of static friction exerted on the crate is $88.2~N$ and this force is directed up the ramp at an angle of $30^{\circ}$ to the horizontal.