You your bicycle have a mass of 80 kg. At the base of a small hill, you are trav

Question

You your bicycle have a mass of 80 kg. At the base of a small hill, you are traveling at 5 m/s along the road. At the top of the hill, you have climbed 5.4 m and are traveling at 1.5 m/s at the top. A) Ignoring friction, what is the total work done on you and the bicycle as you went from the base to the top of the hill? B) At the top of the hill you discover a stop sign and have to stop quickly. The coefficient of static friction for rubber on concrete is 1.0 and the dynamic coefficient of friction is 0.8. Assume that your apply the brakes as of friction as hard as you can without skidding, how for will you travel before stopping? C) Assuming you lock the brakes, how for will you travel before stopping?

Explanation / Answer

here,

speed at bottom , u = 5 m/s

speed at top , v = 1.5 m/s

h= 5.4 m

a)

the work done on me and the bicycle , W = change in total energy

W = m * g * h + 0.5 * m * v^2 - 0.5 * m * u^2

W = 80 ( 9.8 * 5.4 + 0.5 * 1.5^2 - 0.5 * 5^2)

W = 3.3 * 10^3 J

b)

us = 1

the accelration , a = - us * g = - 9.8 m/s^2

v^2 - u^2 =2 * a * s

1.5^2 = 2 * 9.8 * s

s = 0.11 m

c)

the distance travelled before stopping is 0.11 m

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