Answer:
the skier is moving at a speed of 8.38 m/s when she gets to the bottom of the hill.
the internal energy generated in crossing the rough patch is 820.26 J
Explanation:
Given that,
Mass, m = 62 kg,
Initial speed, = 6.90 m/s
Length of rough patch, L = 4.50 m,
coefficient of friction, = 0.3
Height of inclined plane, h = 2.50 m
is the acceleration due to gravity
According to energy conservation equation,
Part (b)
The internal energy generated when crossing the rough patch is equal (in magnitude) to the work done by the friction force on the skier.
The magnitude of the friction force is:
Therefore, the work done by friction is:
The negative sign is due to the fact that the friction force is opposite to the direction of motion of the skier
Substituting,
So, the internal energy generated in crossing the rough patch is 820.26 J
Part (a)
If we take the bottom of the hill as reference level, the initial mechanical energy of the skier is sum of his kinetic energy + potential energy:
After crossing the rough patch, the new mechanical energy is
where
W = -820.26 J is the work done by friction
At the bottom of the hill, the final energy is just kinetic energy,
where v is the final speed.
According to the law of conservation of energy, we can write:
So we find v:
Thus, the skier is moving at a speed of 8.38 m/s when she gets to the bottom of the hill.