A person pushes horizontally with constant force P on a 230 N box resting on a frictionless horizontal floor.
Which of the following statements about this box is correct?
A.The box will accelerate no matter how small P is.
B. The box will not accelerate unless P > 230 N.
C. The box will move with constant velocity because P is constant.
D.Once the box is set moving, it will come to rest after P is removed.
To determine the correct statement about the box, we need to analyze the forces acting on it and the resulting motion.
In this scenario, the person applies a horizontal force P on the box, while the floor exerts an equal and opposite force (normal force) perpendicular to the box's surface. Since the floor is frictionless, there is no frictional force acting on the box.
Now let's evaluate each statement:
A. The box will accelerate no matter how small P is.
This statement is incorrect. According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force acting on it. In this case, the only force acting on the box is the horizontal force P. Therefore, if P is zero or too small, the box will neither accelerate nor move.
B. The box will not accelerate unless P > 230 N.
This statement is incorrect. As mentioned earlier, the net force on the box is equal to the applied force P. If P is greater than zero, the box will experience an acceleration proportional to that force. The mass of the box remains constant (given information). Therefore, even if P is less than 230 N, the box will still accelerate.
C. The box will move with constant velocity because P is constant.
This statement is incorrect. The box will not move with a constant velocity unless the net force acting on it is zero. In this case, the applied force P is not balanced by other forces, so there is a resulting unbalanced force, causing acceleration.
D. Once the box is set moving, it will come to rest after P is removed.
This statement is correct. If the applied force P is removed after the box is set in motion, there will be no net force acting on it. According to Newton's first law of motion (the law of inertia), an object in motion will continue moving with a constant velocity in the absence of external forces. Therefore, when P is removed, the box will gradually come to rest due to the absence of a net force.
So, the correct statement is D. Once the box is set moving, it will come to rest after P is removed.