Newton's second law: On a horizontal frictionless floor, a worker of weight 0.900 kN pushes horizontally with a force of 0.200 kN on a box weighing 1.80 kN. As a result of this push, which statement could be true? A) The box will not move because the push is less than its weight. B) The worker and box will both have an acceleration of 1.08 m/s², but in opposite directions. C) The worker and box will both have an acceleration of 2.17 m/s², but in opposite directions. D) The worker will accelerate at 1.08 m/s² and the box will accelerate at 2.17 m/s², but in opposite directions. E) The worker will accelerate at 2.17 m/s² and the box will accelerate at 1.08 m/s², but in opposite directions.

Question

Quizplus · Accepted Answer

According to Newton's second law, the force applied (0.200 kN) is equal to the product of the mass (1.80 kN) and acceleration (a) of the box. Therefore, a = 0.200 kN / 1.80 kN = 0.111 m/s^2. Similarly, the force on the worker (0.900 kN) is equal to his mass (unknown) times his acceleration (a'). We cannot solve for a' without knowing the worker's mass. However, we know that the total force on the system (box + worker) is 0.200 kN + 0.900 kN = 1.10 kN, and this force is equal to the product of the total mass (1.80 kN + worker's mass) and the acceleration of the system (a + a'). Therefore, a + a' = 1.10 kN / (1.80 kN + worker's mass). Since the floor is frictionless, there is no horizontal force on the system other than the push, so the system will accelerate as a whole. Therefore, the acceleration of the worker and box must be the same magnitude but opposite in direction, so |a'| = |a| = 0.111 m/s^2. Solving for the worker's acceleration using the equation above, we get a' = 2.17 m/s^2. Therefore, the correct answer is E, which states that the worker will accelerate at 2.17 m/s^2 and the box will accelerate at 1.08 m/s^2, both in opposite directions.

Newton's Second Law: on a Horizontal Frictionless Floor, a Worker