A hockey puck of mass 0.27 kg is sliding along a slippery frozen lake, with an initial speed of 56 m/s. The coefficient of friction between the ice and the puck is μK = 0.032. Friction eventually causes the puck to slide to a stop. Find the work done by friction.
The work done by friction is -(1/2) M V^2, no matter what the coefficient of firction is. With a + sign, it is the work that the puck does against friction, which equals the initial kinetic energy.
If you compute the friction force and multiply it by the distance the puck slides before stopping, to get the work done, you will find that ìK cancels out.
To find the work done by friction, we need to know the distance over which the friction acts.
The work done by a force is given by the equation:
Work = Force x Distance x cos(θ)
where Force is the magnitude of the force, Distance is the distance the force acts over, and θ is the angle between the force and the direction of motion.
In this case, the force of friction acts opposite to the direction of motion, so the angle between the force and the direction of motion is 180 degrees, and cos(180 degrees) = -1.
First, we need to find the magnitude of the frictional force using the equation:
Frictional Force = μk * Normal Force
where μk is the coefficient of friction and Normal Force is the force exerted by the surface perpendicular to the direction of motion.
Since the puck is sliding on a flat surface, the Normal Force is equal to the weight of the puck, which is given by:
Normal Force = Mass x Gravity
where Mass is the mass of the puck and Gravity is the acceleration due to gravity (approximately 9.8 m/s^2).
Now we can calculate the frictional force:
Frictional Force = μk * Normal Force
Frictional Force = 0.032 * (0.27 kg * 9.8 m/s^2)
Once we have the frictional force, we can calculate the distance over which the friction acts.
Since the puck eventually comes to a stop, the work done by friction is equal to the initial kinetic energy of the puck. The initial kinetic energy of the puck is given by:
Initial Kinetic Energy = 0.5 * Mass * (Initial Velocity)^2
Finally, we can find the work done by friction:
Work = Frictional Force x Distance x cos(180 degrees)
Work = (-Frictional Force) x Distance
Equating the work done by friction to the initial kinetic energy, we can solve for the distance:
Initial Kinetic Energy = Work
0.5 * Mass * (Initial Velocity)^2 = (-Frictional Force) x Distance
Now we can substitute the known values into the equation and solve for the distance.