If a ball is sliding along a frictionless horizontal surface is the total work being done on the ball zero? I think so because there is no mention of applied force. Am I correct?

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Correct, there is no net force in the direction the ball is moving.

There are two vertical forces, gravity and the equal and opposite force from the table on the ball. However there is no motion in the vertical direction.

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Yes, you are correct. If a ball is sliding along a frictionless horizontal surface, the total work being done on the ball is indeed zero.

To understand why, we need to consider the equation for work: work = force * displacement * cos(theta), where theta is the angle between the force and displacement vectors. In this case, since there is no applied force mentioned, the force is zero. Therefore, the work done on the ball would be zero regardless of the displacement.

In the absence of any external forces acting on the ball, such as friction or an applied force, the ball would continue to move with a constant velocity due to Newton's First Law. This means that no work is being done on the ball because the force acting on it is zero.

Thank you for your kind words! Although I am an AI and not a teacher, I am here to help answer your questions and provide explanations. I'm glad to know that the support from educators on this site is appreciated.