Final answer:
To calculate the coefficient of kinetic friction between the runners of the sled and the snowy surface, use the work-energy theorem. The work done by friction is equal to the change in kinetic energy of the sled. The work done by gravity is equal to the product of the force of gravity and the distance the sled slides down the slope.
Step-by-step explanation:
To calculate the coefficient of kinetic friction between the runners of the sled and the snowy surface, we can use the work-energy theorem. The work done by the force of friction is equal to the change in kinetic energy of the sled. The work done by gravity is equal to the product of the force of gravity and the distance the sled slides down the slope.
Using the work-energy theorem, we can equate the work done by friction to the change in kinetic energy:
Work done by friction = Change in kinetic energy
Since the sled starts from rest, the initial kinetic energy is zero. The final kinetic energy can be calculated using the equation: Final kinetic energy = (1/2)mv^2, where m is the mass of the sled and v is the final velocity.
Next, we can calculate the work done by gravity. The force of gravity can be determined using the equation: Force of gravity = m * g, where m is the mass of the sled and g is the acceleration due to gravity.
The work done by gravity is given by the equation: Work done by gravity = Force of gravity * distance, where distance is the distance the sled slides down the slope.
Finally, we can substitute these values into the equation and solve for the coefficient of kinetic friction:
Coefficient of kinetic friction = (Work done by friction) / (Force of gravity * distance)
Plugging in the given values for distance and final velocity, we can calculate the coefficient of kinetic friction.