Cork Institute of Technology
Higher Certificate in Engineering in Biomedical Engineering – Stage 1
(National Certificate in Engineering in Biomedical Engineering – Stage 1)
(NFQ – Level 6)
Autumn 2005
Engineering Mechanics
(Time: 3 Hours)
Answer Five Questions
Examiners:
All questions carry equal marks
1.
Dr. P. McHugh
Mr. D. Tallon
Dr. K. Bryan
Ms. S. Bryan
Consider the total hip joint prosthesis shown in figure Q1(a).
The geometric parameters of the prosthesis are such that l1 =
50mm, l2 = 100mm, θ1 = 45°, and θ2 = 90°. Assume that,
when standing symmetrically on both feet, a joint reaction
force of 400N is acting at the femoral head. Consider three
different lines of action for the applied force, which are shown
in figure Q1(b).
Determine the moments generated about points B and C on
the prosthesis for all cases shown.
(20 marks)
2.
Based on the assumption that the air resistance is negligible, it
is suggested that the overall motion characteristic of a long
jumper may be analysed by assuming that the centre of gravity
of the athlete undergoes a projectile motion.
Consider an athlete who jumps a horizontal distance of 9m
after reaching a maximum height of 1.5m. What was the
takeoff speed of the athlete? Discuss how the athlete can
improve their performance.
(20 marks)
3.
Consider the split Russel Traction device and the
mechanical model of the leg shown in Figure Q3.
The leg is held in the position shown by two weights
that are connected to the leg via two cables. The
combined weight of the leg and the cast is W = 300
N. l is the horizontal distance between points A and
B where the cables are attached to the leg. C is the
center of gravity of the leg including the cast, which
is located at a distance two-thirds of l as measured
from A. The angle cable 2 makes with the horizontal
is measured as β = 45o.
Determine the tensions T1 and T2 in the cables, weights W1 and W2, and the angle α that
cable 1 makes with the horizontal, so that the leg remains in equilibrium at the position
shown.
(20 marks)
4.
During a practice, a shot-putter puts the shot at a distance l = 6m. At the instant the athlete
releases the shot, the elevation of the shot is ho = 1.8m as measured from the ground level,
and the angle of release is θ =30º.
Fig
Determine the :
1
(i)
speed at which the athlete releases the shot.
(ii)
landing speed of the shot.
(iii) total time the shot was in the air.
(20 marks)
5.
(a) What pressure is at the bottom of an oil tank if the depth
of oil is 1.3m and the relative density of the oil is 0.8?
60
cm 150cm
(4 marks)
(b) A circular gate 125cm in diameter is immersed at some
angle in water so that the vertical distance of its top
∅125cm
Figure Q5
perimeter to the surface of the water is 60cm and the
vertical distance of its bottom perimeter is 150cm. Find the total force due to the water on
one side of the gate if the density of the water is 1000kg/m3.
(16 marks)
6. (a) What is a Venturi meter used for and how does it work?
(5 marks)
(b) A vertical diffuser has an inlet of 60mm diameter and an outlet of 160mm diameter. The
height between the inlet and outlet is 200mm. The velocity at the inlet is 2m/s.
i. What is the volumetric flow rate through the diffuser?
ii. What is the velocity at the outlet?
iii. What is the pressure difference across the device?
2
Bernoulli’s equation
P V2
P1 V12
+
+ z1 = 2 + 2 + z 2
ρg 2 g
ρg 2 g
1
(15 marks)
7. (a) With the aid of a diagram explain absorption, reflection and transmission of radiant heat.
(4 marks)
(b) How long would it taken for a water-bath that is rated at 2kW to heat up 20 litres of water
from 10°C to 37°C?
cwater = 4200 J/kgK
(8 marks)
(c) If 2 litres of water at 95°C were then to be added to the water-bath what would be the final
temperature? Assume that there are no losses.
(8 marks)