1. To determine the force of friction acting on the crate, we need to consider the forces acting on it. Since the crate is at rest on the incline, there are two main forces acting on it: the force of gravity (acting vertically downwards) and the normal force (acting perpendicular to the incline). The force of friction is parallel to the incline (along the surface of the incline) and opposes the motion of the crate. In this case, since the crate is at rest, the force of friction must be equal in magnitude and opposite in direction to the component of the force of gravity parallel to the incline. This means that the force of friction points up the incline, so the answer is (a) The friction force points up the incline.
2. In this situation, the physicist is trying to push the crate up the incline but cannot start its motion. This indicates that the force of friction acting on the crate is greater than the force the physicist is applying. If the crate were to move up the incline, the force of friction would need to be overcome by a greater force. Therefore, the force of friction must be pointing down the incline, opposing the motion, and preventing it from starting. The answer is (b) The friction force points down the incline.
3. When both physicists push on the crate parallel to the surface of the incline, they are exerting a force on the crate that helps overcome the force of friction and keep the crate moving at a constant speed up the incline. According to Newton's third law, the force exerted by the two physicists on the crate must be equal in magnitude and opposite in direction to the force of friction. This means that the force exerted by the two physicists on the crate is equal to the force of friction on the crate. So, the force exerted by the two physicists on the crate is equal to the force of friction.