Download GNG 1100 - ENGINEERING MECHANICS Supplemental

GNG 1100 - ENGINEERING MECHANICS
Supplemental Examination
February 2001
Profs. Droste, Hallett, Mirfakhraei & Skaff
Time: 3 hours
Page 1 of 3
Closed book. All calculators allowed. Free-body diagrams must be drawn wherever appropriate.
1. (8 marks) A professor pushes with a force P
on a desk at the front of the class. The desk
weighs 300 N and its centre of gravity is at G. If
the coefficient of static friction between the desk
legs and the floor is :S = 0.4, calculate the force
P required to make the desk move.
2. (12 marks) The sketch shows a truss
subjected to a load P = 20 kN. All joints are
pinned.
(a) Determine the reactions at the supports A
and D.
(b) Calculate the forces in members AJ, BJ
and BC. State whether each is in tension or
compression.
(c) List all zero-force members in this truss
for the loading shown.
GNG 1100 - ENGINEERING MECHANICS
Supplemental Examination
February 2001
Profs. Droste, Hallett, Mirfakhraei & Skaff
Time: 3 hours
Page 2 of 3
3. (12 marks) Two gears are mounted on a shaft AD and subjected to forces as shown. Gear B has
a radius of 15 cm and is subjected to force Q = 200 N at an angle of 20° to the horizontal, while gear
C has a radius of 5 cm and is subjected to a force P at an angle of 20° to the vertical. Both P and Q
are parallel to the y-z plane. Bearings A and D are aligned with the shaft; bearing A is a thrust
bearing, but bearing D can not carry an axial load. Calculate force P and the reaction components
at the bearings.
4. (8 marks) A 100 kg block is pushed up a 15° slope by a
horizontal force P, as shown in the diagram. If the coefficient
of kinetic friction between the block and the incline is :K =
0.25, find the magnitude of P required to accelerate the block
at a rate of 2 m/s2.
GNG 1100 - ENGINEERING MECHANICS
Supplemental Examination
February 2001
Profs. Droste, Hallett, Mirfakhraei & Skaff
Time: 3 hours
Page 3 of 3
5. (6 marks) The sketch shows the system of pulleys and cables
used in an elevator system. The weight of the elevator car E is
partially balanced by a counterweight W. If the car moves
downwards at a constant speed vE = 3 m/s, determine
(a) the velocity of the cable at point D;
(b) the velocity of the counterweight W;
(c) the relative velocity of the counterweight with respect to the
elevator car.
6. (14 marks) The sketch shows a
robotic gripper or “hand” which can
be made to grip an object by
applying a force P to point A. The
forces R are the reactions to the
object being picked up. All joints
are pinned. The pins at joints D, E
and F are rigidly connected to a
solid support.
(a) Identify all two-force members
in this device.
(b) If the gripping force R = 25 N,
determine all forces on member
BDH and find the actuating force P.
Note: since the device and load are completely symmetrical, you only have to solve the members in
one half. All dimensions are in cm.
Total marks for this paper: 60