An 80.0 kg rollerblader is at rest at the top of a 100 m hill at a 7o incline. The coefficient of friction on the hill is 0.110. What is the roller blader's kinetic energy at the bottom of the hill?
h/d=sin7 d=100/sin7=820.6m v^2=2gd(sin7-0.11cos7)=2*9.8*820.6*0.0127 v=sqrt(204.264) v=14.3m/s k.e at bottom=1/2*80*14.3^28179.6joules
To find the rollerblader's kinetic energy at the bottom of the hill, you need to know the work done on the rollerblader by the force of gravity and the work done against friction.
First, let's calculate the gravitational potential energy at the top of the hill:
Gravitational Potential Energy = mass × gravity × height
= 80.0 kg × 9.8 m/s² × 100 m
= 78,400 J
Since the rollerblader is at rest at the top of the hill, the initial kinetic energy is zero.
Next, let's calculate the work done against friction along the incline. The force of friction can be calculated using the equation:
Force of friction = coefficient of friction × normal force
The normal force is equal to the component of the weight perpendicular to the incline, which is given by:
Normal force = mass × gravity × cosine(incline angle)
In this case, the incline angle is 7°.
Normal force = 80.0 kg × 9.8 m/s² × cos(7°)
= 794.769 N
Force of friction = 0.110 × 794.769 N
= 87.424 N
The work done against friction is given by:
Work against friction = force of friction × distance
The distance traveled along the incline is 100 m.
Work against friction = 87.424 N × 100 m
= 8,742.4 J
Now, you can calculate the rollerblader's kinetic energy at the bottom of the hill using the work-energy theorem:
Work done by all forces = Change in kinetic energy
The rollerblader starts from rest at the top of the hill, so the total work done is equal to the kinetic energy at the bottom of the hill.
Total work done = Gravitational Potential Energy - Work against friction
Kinetic energy at the bottom of the hill = Total work done
= 78,400 J - 8,742.4 J
= 69,657.6 J
Therefore, the rollerblader's kinetic energy at the bottom of the hill is 69,657.6 J.