A 2.2kg bowling ball with a velocity of 2m/s rolls along a level floor for 30m before coming to a halt. What is the coefficient of rolling friction?
To determine the coefficient of rolling friction, we need to use the equation:
Friction force = rolling friction coefficient * normal force
The normal force in this case is equal to the weight of the bowling ball, which can be calculated using the formula:
normal force = mass * acceleration due to gravity
First, let's calculate the normal force:
mass = 2.2kg (given)
acceleration due to gravity = 9.8m/s^2 (approximately)
normal force = 2.2kg * 9.8m/s^2 = 21.56N
Next, we need to determine the initial kinetic energy of the bowling ball. Since it comes to a halt, all of the initial kinetic energy is converted into work done by the friction force. The initial kinetic energy can be calculated as:
initial kinetic energy = (1/2) * mass * velocity^2
velocity = 2m/s (given)
initial kinetic energy = (1/2) * 2.2kg * (2m/s)^2 = 4.4J
Since the work done by friction is equal to the initial kinetic energy, we have:
work done by friction = friction force * distance
substituting the formula for work done by friction:
friction force * distance = (1/2) * mass * velocity^2
Now we can solve for the friction force:
friction force = (1/2) * mass * velocity^2 / distance
plugging in the values:
friction force = (1/2) * 2.2kg * (2m/s)^2 / 30m = 0.2933N
Finally, we can determine the coefficient of rolling friction:
friction force = rolling friction coefficient * normal force
rolling friction coefficient = friction force / normal force
substituting the values:
rolling friction coefficient = 0.2933N / 21.56N = 0.0136
Therefore, the coefficient of rolling friction is approximately 0.0136.