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PST 2019 Sem 2(1)

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EGB211 – 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 𝛼 = 10°, a car with an initial
speed 𝑣0 = 80 π‘˜π‘š/β„Ž, starts to accelerate. The friction coefficient due to the contact of the wheels is
πœ‡ = 0.15. The air resistance in this case needs to be accounted for and is equal to 0.9 𝑣 2 , 𝑣 being the
speed of the car. The force exerted by the motor of the car is denoted by πΉπ‘š .
For this exercise consider a car of mass π‘š = 2,500 kg.
x
slope
π’Ž
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 πΉπ‘š (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‘Ž(𝑑) 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 𝑅 = 10 m, mounted on a 3 m tall vertical shaft (β„Ž = 3 m),
rotating at a constant angular speed πœ”0 = 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 (π‘šπ‘ ), 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 carousel’s 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 Ошибка! Π˜ΡΡ‚ΠΎΡ‡Π½ΠΈΠΊ ссылки
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 (𝑇).
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 (𝑇).
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 πœ‡π΅ will cause the
system to stop moving)?
Answer within the space provided by this box; the box can be expanded if needed