A ball rolls up a ramp and then back down again. The ramp is oriented so that the ball is rolling to the right as it rolls up the ramp. Assume that positive v and a vectors point to the right. Which statement is true about the ball's horizontal acceleration?
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To determine the direction of the ball's horizontal acceleration, we need to look at the forces acting on the ball.
When the ball rolls up the ramp, two forces are acting on it: the force of gravity pulling it downward and the normal force exerted by the ramp pushing it upward.
Since the ball is rolling to the right up the ramp, the normal force is pointing in the opposite direction, to the left. This is because the normal force always acts perpendicular to the surface of contact, which in this case is the ramp.
The force of gravity is always pointing downward, irrespective of the direction of motion. Therefore, the ball's horizontal acceleration is determined by the difference between these two forces.
Since the normal force is pointing to the left and the force of gravity is pointing downward, their horizontal components will add up. So the horizontal acceleration of the ball is the sum of these two components.
Therefore, the statement that is true about the ball's horizontal acceleration is that it is the sum of the horizontal components of the force of gravity and the normal force.