Joe pushes horizontally on a heavy box across a rough surface at constant speed. Which one of the following statements concerning this situation is false?

If Joe stops pushing on the box, the box will stop sliding eventually.

If Joe doubles his force on the box, the speed of the box will double.

The magnitude of the force of kinetic friction acting on the box must be equal to the magnitude of the force that Joe is applying to the box.

If the box were lighter, Joe could apply a smaller force to achieve the same constant speed.

first statement, true

second statement: Nonsense.
third statement true, as long as speed is constant.

thank you! and the fourth statement?

To determine which statement is false, let's analyze each statement one by one:

Statement 1: If Joe stops pushing on the box, the box will stop sliding eventually.
Explanation: This statement is true. According to Newton's first law of motion, an object will continue to move at a constant velocity (in this case, constant speed) unless acted upon by an external force. Once Joe stops pushing on the box, the only external force acting on it would be kinetic friction, which opposes the motion and eventually brings the box to a stop.

Statement 2: If Joe doubles his force on the box, the speed of the box will double.
Explanation: This statement is false. The speed of the box will not necessarily double if Joe doubles his force. The relationship between force and speed is not linear. In this situation, if Joe doubles his horizontal force, the box's acceleration will increase, and it may eventually reach a new constant speed, but not necessarily double its initial speed.

Statement 3: The magnitude of the force of kinetic friction acting on the box must be equal to the magnitude of the force that Joe is applying to the box.
Explanation: This statement is true. According to Newton's third law of motion, every action has an equal and opposite reaction. In this case, the force that Joe applies to the box (pushing horizontally) creates an equal and opposite force of kinetic friction acting on the box in the opposite direction. So the magnitudes of these two forces are equal.

Statement 4: If the box were lighter, Joe could apply a smaller force to achieve the same constant speed.
Explanation: This statement is true. According to Newton's second law of motion, the acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass. If the box were lighter, its mass would be smaller, and therefore, Joe would need to exert a smaller force to achieve the same constant speed.

Therefore, the false statement is:

If Joe doubles his force on the box, the speed of the box will double.