Descriptions of Common Student Difficulties with Forces
Students hold the Aristotelian idea that an object's natural state is rest. Thus they believe that objects only move when a net force is exerted upon them. This stems from common everyday observations, e.g. students seeing that objects which have been pushed across the floor come to a stop (and not seeing friction as a dissipative force acting on the object).
Rather than associating the direction of the net force with the direction of the acceleration, some students think that the object will accelerate in the direction of the force with the largest magnitude.
Some students believe that inert objects cannot exert a force. They can alter an object's motion, but they don't exert a force.
Many students hold that the normal force acting on an object is equal to the weight of the object, regardless of the physical situation. Thus the normal force has an upper (and lower) limit placed on it.
Some students believe in their heart of hearts that force is proportional to velocity. Thus if velocity isn't changing, the net force must be (a non-zero) constant. Furthermore, they associate an acceleration with an increasing force.
Some students believe in their heart of hearts that force is proportional to velocity. Thus if velocity is larger, the net force must be larger. Furthermore, they associate an acceleration with an increasing force.
From common everyday observations, e.g. students pushing on an object which is sliding across the floor, they find the force which will initially accelerate an object produces a constant velocity soon after (due to velocity dependent nature of friction that we all ignore in F = mN). Thus students conclude that the force has been used up by the body.
Some students believe in their heart of hearts that force is proportional to velocity. Thus they assume that net force is in the same direction as velocity. Without seeing acceleration's role in changing the velocities' direction, they assume that the object will travel in a straight line.
Some students believe that if an object repeats a motion, it will (inherently) learn that motion, and continue it regardless of changes in the forces acting on it. For example, a rock spun on a string is believed to continue on a curved path after the string is cut or released.
Just like feathers fall more slowly than rocks, students believe that light objects simply fall slower than heavier objects.
Like the trajectory of a football pass will have the point of the ball pointing in the direction of its velocity, students believe that objects will point in the direction of their velocity (regardless of the forces acting on them). The original motion of the object can define its "point" (which could be one side of a cube).
Many students have difficulty in associating the opposite direction with a change in sign. Some students will insist that forces, like their magnitudes, are always positive.
Some students believe that if two objects are tied together by a (continuously taught) string, while one object is pulled by an external force, the second object experiences a force equal in magnitude to the external force (regardless of its mass).
Students add the magnitudes of the each of the forces acting on strings/ropes and treat that as the tension in the string/rope.