To determine the length of time it takes for the ball to stop rolling, we can use the concept of kinetic friction and Newton's second law of motion.
The force of friction opposing the motion of the ball is given as 2.4 N. This force acts in the opposite direction to the velocity of the ball.
Using Newton's second law, we have:
Net force = mass * acceleration
The net force acting on the ball is the force of friction opposing its motion. Since the ball is rolling on a table, the only significant force acting on it is the force of friction. Therefore, the net force is equal to the force of friction.
2.4 N = 5.5 kg * acceleration
Solving for acceleration:
acceleration = 2.4 N / 5.5 kg ≈ 0.4364 m/s²
Now, we can use the equation of motion to calculate the time it takes for the ball to stop rolling. The equation of motion for linear motion under constant acceleration is:
v = u + at
where: v = final velocity (which is 0 m/s when the ball stops) u = initial velocity (15 m/s) a = acceleration (-0.4364 m/s², negative because it opposes the initial motion) t = time
0 = 15 m/s + (-0.4364 m/s²) * t
Rearranging the equation to solve for time:
t = -15 m/s / -0.4364 m/s² ≈ 34.37 seconds
Therefore, it will take approximately 34.37 seconds for the ball to stop rolling.