When rolling along the felt on the billiard table, the ball experiences a frictional force of 0.2 N.
a. What is the deceleration of the ball on the felt?
b. How far will the ball roll before stopping?
c. Explain this in terms of Newtons first law of motion.
a. To find the deceleration of the ball on the felt, we can use Newton's second law of motion. The equation is given as:
F = m * a
Where:
F is the frictional force acting on the ball (0.2 N),
m is the mass of the ball, and
a is the acceleration of the ball.
Since we are looking for the deceleration, which is the negative acceleration, we can rewrite the equation as:
-0.2 N = m * a
b. To find how far the ball will roll before stopping, we need to use the equation for motion with constant acceleration:
v^2 = u^2 + 2as
Where:
v is the final velocity of the ball (0 m/s since it stops),
u is the initial velocity of the ball (unknown),
a is the deceleration of the ball (which we found in part a),
s is the distance traveled by the ball before stopping (unknown).
Rearranging the equation, we get:
0 = u^2 + 2as
Since the final velocity is 0, we can simplify the equation to:
u^2 = -2as
c. According to Newton's first law of motion, an object will remain at rest or continue to move with constant velocity unless acted upon by an external force. In this case, the ball is experiencing a frictional force on the felt, which is acting as an external force.
Initially, the ball is rolling with some velocity on the table. However, due to the frictional force opposing its motion, the ball decelerates. Eventually, the ball comes to a stop when the frictional force overcomes its initial velocity. The frictional force acts in the opposite direction to the motion of the ball, causing it to slow down.
This is in accordance with Newton's first law because the ball continues moving until an external force (friction) acts on it, causing it to decelerate and eventually come to a stop.