Answer:
Therefore, the shuffleboard disk will travel a distance of 4.71 meters before coming to a stop, which is less than the length of the court (14.3 meters).
Explanation:
We can start by using the work-energy principle, which states that the net work done on an object is equal to its change in kinetic energy. In this case, we can assume that the initial kinetic energy of the disk is entirely converted to work done by friction, which causes the disk to come to a stop. The equation can be written as:
Work done by friction = Change in kinetic energy
The work done by friction can be calculated using the formula:
Work = force x distance
The force of friction can be found using the formula:
Force of friction = coefficient of friction x normal force
The normal force is equal to the weight of the disk, which can be found using the formula:
Weight = mass x gravity
Substituting the values given in the problem, we get:
Weight = mass x gravity = 0.75 kg x 9.81 m/s^2 = 7.3575 N
Force of friction = coefficient of friction x normal force = 0.34 x 7.3575 N = 2.4985 N
Work done by friction = Force of friction x distance
We can solve for the distance by rearranging the equation as:
Distance = Work done by friction / Force of friction
The initial kinetic energy of the disk can be found using the formula:
Kinetic energy = 0.5 x mass x velocity^2
Substituting the values given in the problem, we get:
Kinetic energy = 0.5 x 0.75 kg x (5.6 m/s)^2 = 11.76 J
Using the work-energy principle, we know that the work done by friction is equal to the change in kinetic energy, which is:
Work done by friction = Kinetic energy = 11.76 J
Substituting this value and the force of friction into the distance formula, we get:
Distance = Work done by friction / Force of friction = 11.76 J / 2.4985 N = 4.71 m
Therefore, the shuffleboard disk will travel a distance of 4.71 meters before coming to a stop, which is less than the length of the court (14.3 meters).