EGB211 β Problem solving Task Solve all the following exercises, showing all the steps of your calculations and solutions. A total of 25 points are split among the three exercises as specified in each exercise title. Please highlight the final answers to each part of each question. Submit your solutions using Turnitin. If you have any technical issue at the moment of the Turnitin submission, please send a copy of your solutions via email at [email protected] within the assignment deadline. Exercise A. A car on a hill (8 points) At the start of a hill, whose slope has an almost constant inclination of πΌ = 10°, a car with an initial speed π£0 = 80 ππ/β, starts to accelerate. The friction coefficient due to the contact of the wheels is π = 0.15. The air resistance in this case needs to be accounted for and is equal to 0.9 π£ 2 , π£ being the speed of the car. The force exerted by the motor of the car is denoted by πΉπ . For this exercise consider a car of mass π = 2,500 kg. x slope π Ξ± = 10° 1. Draw the free body diagram of the car during the climb of the hill and draw your selected coordinate system. Answer within the space provided by this box; the box can be expanded if needed 2. Obtain the equation of motion of the car as a function of the only unknowns π₯ (and/or its derivatives) and πΉπ (i.e. express all other quantities numerically) Answer within the space provided by this box; the box can be expanded if needed 3. Given that the car acceleration π(π‘) is constant and equal to 1m/s2, obtain the analytical expression of motor power in time. Assuming the maximum power of the car is 425kW, for how long can the car maintain such an acceleration? Answer within the space provided by this box; the box can be expanded if needed Exercise B. Carousel Accident (7 points) An accident, luckily with no casualties, happens at an amusement park. The accident involves a highspeed carousel, composed of: ο· A series of radial arms of radius π = 10 m, mounted on a 3 m tall vertical shaft (β = 3 m), rotating at a constant angular speed π0 = 2.5 rad/s ο· a series of seats attached to the at the free ends of each arm (negligible mass) One of the seats, carrying a 65 kg passenger (ππ ), brakes during operation at nominal speed. The passenger is therefore released and after a short flight, he lands on a pop-corn kiosk (of negligible height), luckily unharmed. An investigation has been opened and you, as a member of the investigation committee, have been asked to reconstruct the details of the accident. The carousel and pop-corn kiosk are installed on flat ground (ie. the base of the shaft is aligned with the kiosk). 1. What was the radial tension on the arm due to the mass of the passenger immediately before the accident occurred? (Show all working. INCLUDE A FBD) Hint: What forces are there in the system? Answer within the space provided by this box; the box can be expanded if needed 2. What was the velocity of the passenger just before the accident? Answer within the space provided by this box; the box can be expanded if needed 3. What was the initial distance between the kiosk and the carouselβs shaft? Answer within the space provided by this box; the box can be expanded if needed Exercise C. A pulley problem (10 points) In this problem we are interested in the pulley-mass system shown in ΠΡΠΈΠ±ΠΊΠ°! ΠΡΡΠΎΡΠ½ΠΈΠΊ ΡΡΡΠ»ΠΊΠΈ Π½Π΅ Π½Π°ΠΉΠ΄Π΅Π½.. Figure 1 1. Draw individual free body diagram for mass A and mass B. ο· Ensure you identify the correct direction of the friction forces. Logically justify your selected friction direction (1 sentence with some supporting calculations). Answer within the space provided by this box; the box can be expanded if needed 2. Derive an equation of motion for mass A in terms of its acceleration and the cable tension (π). Answer within the space provided by this box; the box can be expanded if needed 3. Derive an equation of motion for mass B in terms of its acceleration and the cable tension (π). Answer within the space provided by this box; the box can be expanded if needed 4. Derive an equation for the constrained motion of the pulley which defines the acceleration of mass A and mass B. ο· Show a diagram to assist in your working. Answer within the space provided by this box; the box can be expanded if needed 5. What are the accelerations of mass A and B? What is the tension in the pulley? Answer within the space provided by this box; the box can be expanded if needed 6. What is the critical friction between the slope and mass B (i.e. what value of ππ΅ will cause the system to stop moving)? Answer within the space provided by this box; the box can be expanded if needed