Situation: During winter, snowstorms in Montreal can change the road conditions in a matter of minutes. The roads become slippery as the coefficient of friction of the road changes with temperature, snow, and ice conditions. It 1s desirable to analyze the problem to help road users understand the physics of the phenomenon. To achieve your goal, you need to apply the correct kinematic techniques using the physical equations to relate displacement, velocity, acceleration, and time. In addition, you are required to select the ideal kinetic technique for the defined situation. Illtps:.-'f'www.y'outube.cu-n:'wz;lch'h'- (IBhhsEuY XZ0Q Problem Description: Bus drivers often need to drive up or down a hill in Montreal. Some of these buses are rear-wheel driven (motor torque only transfers to rear wheel; front wheel spins freely). Your job is to describe the forces involved in a bus travelling up or down a 20 inclined hill. The two conditions are: 1) Driving up the hill Hint: assume that the bus is a rear-wheel drive, accordingly friction 1s only applied to the rear wheels. (1.e., front wheels do not have friction). 2) Braking down the hill Hint: brakes are applied to lock all wheels; accordingly, all wheels have friction. For BOTH of the Two Conditions Above: a) Draw the free body diagrams of the bus with its passengers. b) Determine if/how the number of passengers (n,) on the bus affects whether the bus can move up or down the hill in a controlled manner at constant velocity under the following road conditions: Dry road: u; = 0.7 and u, = 0.6 e Wet road: y; = 0.55 and y;, = 0.4 e Icyroad: u, = 0.15 and y;, = 0.1 e Hints: 1. You may need to find the proportional loading of each wheel 1. Recall that friction 1s a reactive force where F =y, N 1s the maximum threshold for no slip iii. A negative n, is not necessarily incorrect. Please think about what it means. ) Describe in your own words what 1s the meaning of the numbers found, according to the situation described above. Case Study Analysis: . There is a total of 6 cases to analyze: 3 with driving up and 3 with braking down. . Your case study needs to include the analysis of all the cases while the bus is going up and down, in the three illustrated road conditions (dry, wet, and icy). Bus Specification (2D): . Length: 12.19 m and Height: 4.38 m (includes height of wheel) . Mass: 11000 kg (mass uniformly distributed in the bus) . Wheels: 2 m from front and back People on Board: . Driver: 1 person, 80 kg, located at I'm from the front 0.38 m . Passengers: no persons, 60 kg per person, assume equivalent point mass of all passengers is located at 3 meters from the back of the bus. . Height-wise, the center of mass of all persons is located in the 0 =20' middle of the bus (i.e., h = 4.38/2 = 2.19 m from the ground). Hibbeler Engineering Mechanics: Dynamics, Fourteenth Edition, Pearson, 2016