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?
b. The ball has a positive acceleration when rolling up the ramp and a negative acceleration when rolling down the ramp.
c. The ball has a positive acceleration when rolling both up and down the ramp.
d. The ball has a negative acceleration when rolling up the ramp and a positive acceleration when rolling down the ramp.
e. The ball has a negative acceleration when rolling both up and down the ramp.
none of the above
acceleration is the change in velocity.
does velocity increase or decrease when rolling up/down the ramp?
c. The ball has a positive acceleration when rolling both up and down the ramp.
The correct answer is:
b. The ball has a positive acceleration when rolling up the ramp and a negative acceleration when rolling down the ramp.
To determine the ball's horizontal acceleration as it rolls up and down the ramp, we need to consider the forces acting on the ball.
When the ball rolls up the ramp, the force of gravity acts vertically downward while the normal force from the ramp acts perpendicular to the surface of the ramp. The ball's weight (mg) can be decomposed into two components, one parallel to the ramp and one perpendicular to the ramp. The component parallel to the ramp is responsible for the ball's acceleration.
Since the ramp is oriented such that the ball is rolling to the right, the component of weight parallel to the ramp points to the right. Thus, the ball experiences a positive acceleration as it rolls up the ramp.
When the ball rolls back down the ramp, the force of gravity and the normal force still act on it, but now the ramp is oriented opposite to the previous case. The component of weight parallel to the ramp now points to the left. Therefore, the ball experiences a negative acceleration as it rolls down the ramp.
Hence, the correct statement is:
b. The ball has a positive acceleration when rolling up the ramp and a negative acceleration when rolling down the ramp.