1. The contestants at a cycling race travel around a 0.5km radius track. The peloton travels 33 laps in 1 hour to complete the race. What is the total angular distance they have traveled? On the first lap, they start from rest and after traveling 3' the circumference of the course, they are traveling at 50 km/h. Assuming a constant acceleration of the peloton, how long did it take them to reach that point?
2. A cyclist of mass 65kg has an unfortunate incident while traveling at v→ = 45km/h i^. The cyclist hits the ground and in 0.1s changes to v→ = 20 km/h i^ + .1 km/h j^. What is the average force of the ground on the cyclist in the x direction?
3. Two cyclists of equal mass of 70kg arrive perpendicular to each other at an intersection and collide completely inelastically. Cyclist 1 was traveling at 15 km/h and cyclist 2 was traveling at 19 k/m. Describe their new velocity (0) just after collision in unit vector notation.
4_ Three cyclists travel in a pace line held in place by magic massless rods. Find the center of mass of the group if their position vectors are given as:
m1 = 90kg r1→ = 5.0mi^, m2 = 120kg r2→ = (5.1 i^+ 0.25j^)m,
m3 = 92kg r3→ = (4.81 i^ - 0.40j^)m
5. A cyclist is on a rolling stationary trainer pedaling such that his wheels are traveling at 30 km/h. He has an unfortunate incident and ends up falling over 90' on his side onto a large patch of ice. Given the cyclist and bicycle have an 1 = 4.5 kg • m2, find the angular velocity that the cyclist will have on the ice after he is on his side? Assume there is negligible mass in the hub and the spokes of the wheels.
6. A cyclist is attached to a rope which is looped over a pulley (disc of mass 10kg and radius 0.5m). The rope is then attached to a hanging block of mass 5kg. What force must the cyclist generate such that the block will move with an acceleration of 2.25 misi. Let's make the assumption that only one wheel of the bicycle is necessary to generate the force (we can ignore the front wheel) and that all the force will manifest itself in rolling friction. The mass of the bicycle and the cyclist is 90kg. The surface has a coefficient of static friction of 0.65 and kinetic friction of 0.25.
