1. A bicyclist uniformly increases his pedaling from 30 rev/min to 120 rev/min in 5.0 s. For that time interval determine:
   (a) the linear acceleration of the bike,
   (b) the final linear speed of the bike, and
   (c) the distance traveled by the bike.
   As shown in the diagram below, the pedal gear has a radius of 12.0 cm, the back wheel gear has a radius of 3.5 cm, and the back wheel itself has a radius of 38.0 cm.
   
   

2. Two blocks are connected by a rope wound around an ideal massless, frictionless, pulley as shown in the diagram below. The mass of the top block is m₁ = 5.0 kg. The mass of the second block is m₂ = 25.0 kg. The coefficient of kinetic friction between the two blocks is µ_blocks= 0.22. The coefficient of kinetic friction between the bottom block and the incline is µ_incline = 0.14. The incline makes an angle of θ = 35.0° with the horizontal. Determine the acceleration of the blocks while they remain in contact.
   

3. A softball player throws a ball at a speed of v₀ = 25 m/s at an angle θ= 55.0° over a split-level building. The front higher part of the building has a height H = 8.7 m. The lower part has a height h = 4.0 m. The player notices that the pitch just misses the front edge of the building as shown in the diagram below.
   (a) How far away, x, is the front of the building?
   (b) How far away, L, does the ball land?
   (c) How long was the ball in the air?
   
   

4. In short sprints, runners can be assumed to maintain constant speeds. In a practice run, runner 1 whose speed is 11.0 m/s, starts the race 5.0 m behind runner 2 whose speed is 10.5 m/s. Despite the headstart, runner 1 wins the race by a distance of 1.0 m.
   (a) Provide a neat sketch of the position versus time graph for the runners.
   (b) How long did the race last?
   (c) How far did each runner travel?
   

5. A car is traveling at a constant speed of 90 km/h over a series of rolling hills and valleys. These hills and valleys follow circular arc. As the driver crests the first hill, he notices a sign which reads "Newton Hill - R = 200 m". At the bottom of the next valley, he is disappointed by the lack of a road sign for the valley. However, since he feels twice as heavy at the bottom of the valley as he feels at the top of the hill, he deduces the radius of curvature of the valley on his own. What is that radius of curvature?
   
   

6. Two blocks m_A = 15.0 kg and m_B = 3.0 kg are connected by a massless rope and two massless, frictionless, pulleys as shown in the diagram below.
   (a) If block A move to the right a distance x, how far down will block B move. From this, if the acceleration of block A is a , what is the acceleration of block B?
   (b) The coefficient of sliding friction between block A and the surface is µ = 0.25. Determine the acceleration of each block.
   (c) Determine the tension in the rope.
   
   

Questions? mike.coombes@kwantlen.ca