Question

Exercise 1

A bicycle rides an inclined plane with an initial velocity 15 m/s. 500 N

a) What is the velocity of the bicycle when it costs a net high of h=5m? We neglect friction
b) What maximum high h that could be reached by the bicycle?

Answer 1

a)

v_i = initial velocity = 15 m/s

v_f = final velocity = ?

h = height gained = 5 m

m = mass

Using conservation of energy between Top and bottom

Kinetic energy at top + potential energy at top = Kinetic energy at bottom

(0.5) m v_f² + mgh = (0.5) m v_i²

v_f² + 2gh = v_i²​​​​​​​

v_f²  + 2 (9.8) (5) = (15)²​​​​​​​

v_f = 11.3 m/s

b)

H = maximum height gained

Using conservation of energy between Top and bottom

potential energy at top = Kinetic energy at bottom

mgH = (0.5) m v_i²​​​​​​​

gH = (0.5) v_i²​​​​​​​

(9.8) H = (0.5) (15)²​​​​​​​

H = 11.5 m