Machines

1
Machines

• Given the magnitude of P, determine the magnitude
  of Q.

2
A Tower Crane
Sample Problem 11.1

• A crane must be in static equilibrium with
  respect to forces and torques or itll tip!
• The crane at right is about to lift a 2800kg
  load. When the load is first lifted where must
  the 9500kg counterweight be located? What is the
  maximum load that can be lifted when the counter
  weight is fully extended?

3
Sample Problem 11.1

• First we go to a free-body diagram for the BEAM
  and find forces and locations.
• The load counterweight act downward and the
  normal force from the tower upward. These three
  forces must cancel to avoid acceleration.
• That is SFyFN-Mg-mg 0 ?FN(Mm)g1.2x105N
• The toques must also sum to 0 for static
  equilibrium
• StMg(x)-mg(7.7m)0?
• xm(7.7m)/M
• (2800kg)(7.7m)/9500kg 2.3m

• The maximum load must have the counterweight at
  its maximum extent, the torque equation is then
• StMg(3.4m)-mg(7.7m)0?
• mM(3.4m)/(7.7m)
• (9800kg)(3.7m)/7.7m4200kg.

4
Sample Problem 11.2
This truss was built to support an escalator. To
find the loads on the truss it was assumed that
the escalator is uniformly filled with people
from the bottom to the top and that two such
trusses (one on either side) support the
escalator.
Force P 1800 N Length a 1 m Length b 1.2 m
Use the Method of Section to determine the force
in the member 45?
5
Sample Problem 11.2

• Considering the free body diagram for the entire
  truss and resolving the forces horizontally and
  vertically, and taking moments about joint 1 we
  obtain

Force P 1800 N Length a 1 m Length b 1.2 m
6
Sample Problem 11.2

• Let us denote ?657 by a. Then passing a section
  through members 35, 45, 46 and taking the upper
  section (567) as a free body we obtain from the
  conditions for static equilibrium the following

Force P 1800 N Length a 1 m Length b 1.2 m
This result is rather surprising. The only other
zero-force member of this truss is member 34. One
can show that these two members are always
zero-force members regardless of the values of
force P and the lengths a and b.
7
Example 12 The figure shows the bones and biceps
in the arm of a person supporting a mass of 2 kg.
Given the weight of the forearm is 9
N,a) determine the tension in the biceps muscle
AB?
TAB
8
Example 13 The figure shows a pair of pliers,
which is a machine designed to exert a large
force on a small object trapped in its jaws. We
analyse the device by breaking it down into the
free-body diagrams of its basic parts, as shown
below.