The statement about needing exactly 100 N of force to push a 300 N box up the ramp is false because it ignores factors such as friction and the efficiency of the ramp. The statement that friction varies with surface roughness or smoothness is true.
The force required to push an object up an inclined plane depends on various factors, and not solely the height and length of the ramp. To conclude that exactly 100 N of force was required, other factors such as friction and the efficiency of the ramp must be considered. Therefore, the statement is False.
Friction does indeed vary from surface to surface. This is because different materials have varying degrees of roughness or smoothness, affecting the amount of resistance an object encounters when moving across these surfaces. This supports the statement that friction varies due to different surface properties as being True.