Final answer:
To find the average coefficient of friction, we can use the work-energy principle. The work done by friction is equal to the change in kinetic energy, which can be calculated using the given values. By equating the work done by friction to the work done against gravity, we can solve for the average coefficient of friction. Average coefficient of friction ≈ -0.41
Step-by-step explanation:
To find the average coefficient of friction, we can use the information provided. The skier reaches the foot of the incline with a speed of 11.0 m/s and glides 15 m up the slope before coming to rest. We can start by finding the work done by friction to bring the skier to a stop. The work done by friction is equal to the change in kinetic energy, which can be calculated using the formula:
Work done by friction = change in kinetic energy
Work done by friction = (1/2) * mass * (final velocity)^2 - (1/2) * mass * (initial velocity)^2
Since the skier comes to rest, the final velocity is 0 m/s. Plugging in the given values, we have:
Work done by friction = (1/2) * 60.0 kg * (0 m/s)^2 - (1/2) * 60.0 kg * (11.0 m/s)^2
Simplifying this expression yields:
Work done by friction = -3630 J
Next, we can find the work done against gravity as the skier glides up the incline. The work done against gravity is given by:
Work done against gravity = mass * g * height
Plugging in the given values, we have:
Work done against gravity = 60.0 kg * 9.8 m/s^2 * 15 m
Simplifying this expression yields:
Work done against gravity = 8820 J
Since the skier comes to rest, the net work done on the skier is equal to zero. Therefore, the work done by the friction force must be equal to the work done against gravity. Setting these two expressions equal to each other, we have:
-3630 J = 8820 J
Finally, we can solve for the average coefficient of friction using the equation:
average coefficient of friction = Work done by friction / (normal force * distance)
Solving for the normal force, we have:
normal force = mass * g
Substituting in the given values, we have:
normal force = 60.0 kg * 9.8 m/s^2
Simplifying this expression yields:
normal force = 588 N
Substituting the known values into the equation for the average coefficient of friction, we have:
average coefficient of friction = -3630 J / (588 N * 15 m)
Simplifying this expression yields:
average coefficient of friction ≈ -0.41