Question

Suppose a 215 kg motorcycle has two wheels and is heading toward a hill at a speed of 30.0 m/s. Assume the wheels to be approximately an annular ring with an inner radius of R1 = 0.280 m and an outer radius of R2 = 0.500 m. The mass of each wheel is 18.3 kg. (a) How high can it coast up the hill in meters, if you neglect friction? (Give your answer to at least 1 decimal place.) m (b) How much energy, in joules, is lost to friction if the motorcycle only gains an altitude of 35.0 m before coming to rest? J

Answer 1

here,

mass of motorcycle , m1 = 215 kg

initial speed , u1 = 30 m/s

R1 = 0.28 m , R2 = 0.5 m

mass of wheel , m2 = 18.3 kg

a)

let the maximum height be h

using conservation of energy

KEt + KEr = m1 * g * h

(0.5 * m1 * u1^2 ) + ( 2 * (0.5 * m2 * (R2^2 - R1^2)) * w^2) = 215 * 9.81 * h

(0.5 * 215 * 30^2 ) + ( 2 * (0.5 * 18.3 * (0.5^2 - 0.28^2)) * (30/0.5)^2) = 215 * 9.81 * h

solving for h

h = 51.2 m

the maximum height is 51.2 m

b)

when h' = 35 m

the energy lost due to friction , U = m1 * g * ( h - h')

U = 215 * 9.81 * ( 51.2 - 35) J

U = 3.42 * 10^4 J