Imagine yourself seated on a wheeled desk chair at your desk. Consider friction forces between the chair and the floor to be negligible. However, the friction forces between the desk and the floor are not negligible. When sitting at rest, you push horizontally against the desk, and the chair rolls backward away from the desk. (a) Which force was responsible for your acceleration. (b) What is the reaction force to the force that caused your acceleration? (c)Explain why the desk did not accelerate. Does this violate Newton’s third law? Explain.

(a) The desk pushing against your hand

(b) Your hand, pushing the desk.
(c) The force applied to the desk was less than the amount necessary to overcome static friction. The desk is heavy and has a high static friction coefficient where the legs touch the floor.
Newton's law is not violated. The desk does not move because the force applied to it by the hand equals the static friction force at the floor. The chair moves because it has wheels and low friction, less than the applied force.

Thank you very much

(a) The force responsible for your acceleration is the force you apply on the desk by pushing horizontally. This force causes the chair to roll backward away from the desk.

(b) The reaction force to the force that caused your acceleration is the force that the desk exerts on you. According to Newton's third law of motion, for every action, there is an equal and opposite reaction. So, when you push the desk, the desk pushes you back with an equal and opposite force.

(c) The desk did not accelerate because of the friction force between the desk and the floor. While you push the desk backward, the friction force between the desk and the floor acts in the opposite direction, preventing the desk from moving. This does not violate Newton's third law because even though the desk does not accelerate, the reaction force it exerts on you still exists and is equal in magnitude but opposite in direction to the force you applied on the desk.

(a) The force responsible for your acceleration is your pushing force against the desk. As per Newton's second law of motion, acceleration is directly proportional to the force applied. In this case, your pushing force creates an acceleration in the opposite direction, causing the chair to roll backward away from the desk.

(b) The reaction force to the force that caused your acceleration is the force exerted by the desk on you. According to Newton's third law of motion, for every action, there is an equal and opposite reaction. So when you push against the desk, the desk reacts by exerting a force on you in the opposite direction.

(c) The desk does not accelerate because of the non-negligible frictional forces between the desk and the floor. When you push against the desk, the frictional force between the desk and the floor opposes the motion. This frictional force counteracts your pushing force, resulting in no net force on the desk. Therefore, the desk does not accelerate.

This situation does not violate Newton's third law. Even though the desk exerts a reaction force on you, the desk and you are separate objects, so the forces acting on each object can have different magnitudes and effects. The reaction force of the desk on you does not directly influence the motion of the desk itself.