UNIVERSITY of PLYMOUTH

 

MECH115: Engineering Science 1

 

Tutorial examples: - Modelling & Systems                           [Use g = 9.81 m/s² where required]

 

 

  1. A crow bar is used to apply high forces to objects. If a typical crow bar is 900 mm long and its working fulcrum is 19mm from one end what force can it apply if 90% of body weight is applied at the other end. Assume an average human body has a mass of 65kg.
    How accurate do you think your prediction is?    [26,610 N]

 

  1. A car of mass 1120 kg has an engine rated at 75kW maximum. Assuming all of its engine power is available, at what rate (in m/s2) can it accelerate when its speed is 1mph, 10 mph and 60 mph. How accurate do you consider your calculated accelerations, and which acceleration will be felt most?   [149.7, 15.0, 2.5 m/s2 ]

 

  1. A pneumatic cylinder has a piston diameter of 25mm, and a actuator shaft diameter of 10mm. If compressed air at a pressure of 7 bar(gauge) is applied to each end of the cylinder in turn calculate the force that the actuator shaft can apply in both the forwards and backwards directions. Are these forces likely to be over or under estimated?  [344 N, 289 N] (Note: the solution is in error, it should read that the force is over estimated)

 

  1. The ultimate tensile stress (UTS) required to break copper wire is 230 MN/m2. Copper fuse wire comes in diameters of 0.230 mm (5A), 0.533 mm (15A) and 0.864 mm (30A). If an average human male can apply a tension of 100N with his hands, which amperage of fuse wire will he be unable to break by hand.    [30A]

 

  1. A weight W, hung centrally on a light string with its ends supported horizontally, as shown below, causes the string to form a 'Vee' shape with an included angle 2q.




    The tension in the string is given by:-



    For a weight of 10 N, sketch a graph of the tension vs. q for the range 0 to 90.
    Comment on how good this model is, especially as 2q approaches 180.

 

  1. If an object is accelerating at a constant rate a, the following equations apply:-

                                                                 

 

 

 

where   u = initial velocity, v = final velocity, a = acceleration, t = time, s = distance.

A car accelerates uniformly from rest to 60 mph in 7 seconds. Find (in standard SI units) its acceleration and the distance it covers. Which assumption is most likely to be in error?
                                                                                                            [3.83 m/s2, 93.9 m]

 

 

  1. The cable and pulley system shown below is used to raise a hinged door of mass 40kg.
    At the position shown find the tension required to raise the door a small amount assuming:-
    (a) no friction in the pulleys, and
    (b) assuming each pulley requires a tension difference of 3.7 N to rotate it.
    In percentage terms what effect does the friction have? Which is the more realistic model?
                                                                                        [196.2 N, 203.6 N, 3.8% increase]










  2. The pressure, volume, mass and temperature of a gas are related by the perfect gas equation:-

 

Find the mass (in kg) of Oxygen in a typical gas cylinder of volume 50 litres, pressure 55 bar, and temperature 20C given that R for Oxygen is 0.260 kJ/kgK.
How would you test this model for accuracy? [3.61 kg]



  1. For an incompressible fluid flowing in a tube the fluid pressure (p), fluid velocity (v) and height above a horizontal datum (h) are related by:-




    To check the model an experiment using water [ r = 1000 kg/m³ ] was done, and the following readings were taken at two different points along the tube:-

 

p(kPa)

v(m/s)

h(m)

200

5.0

0

101

11.1

4.2


How good is the model (in percentage terms)?
What do you think might cause any difference between the two points along the tube?

                                     [constant = 21.662 m & 20.775 m respectively, giving a -4.1 % error]

 

 

115tut_modeling&systems