A girl on a bike is moving at a speed of 1.40 m/s at the start of a 2.45 m high and 12.4 m long incline. The total mass is 60.0 kg, air resistance and rolling resistance can be modeled as a constant friction force of 41.0 N, and the speed at the lower end of the incline is 6.70 m/s. Determine the work done (in J) by the girl as the bike travels down the incline.

Explanation:

Given that,

Initial speed of the girl is

u = 1.4m/s

Height she is going is

H = 2.45m

Incline plane she will pass to that height

L = 12.4m

Mass of girl and bicycle is

M=60kg

Frictional force that oppose motion is

Fr = 41N

Speed at lower end of inclined plane

V2 = 6.7m/s

Work done by the girl when the car travel downward

Using conservation of energy

K.E(top) + P.E(top) + work = K.E(bottom) + P.E(bottom) + Wfr

Where Wfr is work done by friction

Wfr = Fr × d

P.E(bottom) is zero, sicne the height is zero at the ground

K.E is given as ½mv²

Then,

½M•u² + MgH + W = ½M•V2² + 0 + Fr×d

½ × 60 × 1.4² + 60×9.8 × 2.45 + W = ½ × 60 × 6.7² + 41 × 12.4

58.8 + 1440.5 + W = 1855.1

W = 1885.1 —58.8 —1440.5

W = 355.8 J