Final answer:
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-energy theorem states that the work done on an object is equal to the change in its kinetic energy. By calculating the initial and final kinetic energies of the sled and finding the work done on the sled, we can then use the equation for work done by friction to solve for the coefficient of kinetic friction.
Step-by-step explanation:
To calculate the coefficient of kinetic friction, we can use the work-energy theorem. The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy.
- First, we need to find the initial and final kinetic energies of the sled. The initial kinetic energy is zero since the sled starts from rest. The final kinetic energy can be calculated using the formula KE = (1/2)mv^2, where m is the mass of the sled and v is its final velocity.
- Next, we can calculate the work done on the sled by subtracting the initial kinetic energy from the final kinetic energy.
- Finally, we can use the equation for the work done by friction, W = μkN, where μk is the coefficient of kinetic friction and N is the normal force. The normal force can be found using N = mgcosθ, where m is the mass of the sled, g is the acceleration due to gravity, and θ is the angle of the incline.
- Substitute the values of the known variables into the equation for work done by friction and solve for the coefficient of kinetic friction, μk.