Suppose a 185 kg motorcycle is heading toward a hill at a speed of 29 m/s. The two wheels weigh 12 kg each and are each annular rings with an inner radius of 0.280 m and an outer radius of 0.330 m. Randomized Variables
m = 185 kg
v = 29 m/s
h = 32 m
A. How high can it coast up the hill. if you neglect friction in m?
B. How much energy is lost to friction if the motorcycle only gains an altitude of 33 m before coming to rest?

A) The motorcycle can coast up the hill by ; 42.86m  

B) The amount of energy lost to friction :  17902.45 J

A) Determine how high the motorcycle can coast up the hill when friction is neglected

apply the formula for kinetic and potential energies

K.E = 1/2 mv²   ( 1 )

P.E = mgH   ( 2 )

As the motorcycle goes uphiLl the kinetic energy is converted to potential energy.

∴ K.E = P.E

1/2 * mv² = mgH

∴ H = ( 1/2 * mv² ) / mg   ( 3 )

where ; m = 185 kg ,  v = 29 m/s ,  g = 9.81

Insert values into equation ( 3 )

H ( height travelled by motorcycle neglecting friction ) =  42.86m  

B) Determine how much energy is lost to friction if the motorcycle attains 33m before coming to rest  

P.E = mgh = 185 * 9.81 * 33  = 59890.05 J

where : h = 33 m , g = 9.81

K.E = 1/2 * mv² = 77792.5 J   ( question A )

∴ Energy lost ( ΔE ) =  ( 77792.5  - 59890.05 ) = 17902.45 J

Hence we can conclude that The motorcycle can coast up the hill by ; 42.86m , The amount of energy lost to friction :  17902.45 J.

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a) Height reached before coming to rest is 42.86 m

b) Energy lost to friction is 17902.45 J

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 = 42.86 m

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 = 17902.45 J

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