Answer:
<em>a) Height reached before coming to rest is 42.86 m</em>
<em>b) Energy lost to friction is 17902.45 J</em>
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Explanation:
mass of the motorcycle = 185 kg
speed of the towards the hill = 29 m/s
The wheels weigh 12 kg each
Wheels are annular rings with an inner radius of 0.280 m and outer radius of 0.330 m
a) To go up the hill, the kinetic energy of motion of the motorcycle will be converted to the potential energy it will gain in going up a given height
the kinetic energy of the motorcycle is given as
=
where m is the mass of the motorcycle
v is the velocity of the motorcycle
=
= 77792.5 J
This will be converted to potential energy
The potential energy up the hill will be
= mgh
where m is the mass
g is acceleration due to gravity 9.81 m/s^2
h is the height reached before coming to rest
= 185 x 9.81 x m = 1814.85h
equating the kinetic energy to the potential energy for energy conservation, we'll have
77792.5 = 1814.85h
height reached before coming to rest = 77792.5/1814.85 = <em>42.86 m</em>
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b) if an altitude of 33 m was reached before coming to rest, then the potential energy at this height is
= mgh
= 185 x 9.81 x 33 = 59890.05 J
The energy lost to friction will be the kinetic energy minus this potential energy.
energy lost = 77792.5 - 59890.05 = <em>17902.45 J</em>
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