STATIC EQUILIBRIUM: FORCES AND TORQUES - Ryerson ...

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STATIC EQUILIBRIUM: FORCES AND TORQUES
OBJECTIVE:
To study the role of forces and torques for an object in equilibrium.
INTRODUCTION:
For an object to be in static equilibrium (zero acceleration and zero velocity) two conditions have to be
satisfied:
1. The sum of all external forces must be zero:
2. The sum of all torques (calculated with respect to an arbitrary common point) must be zero:
Torque is a quantity that measures the tendency of an applied force to cause rotation. Torque depends not only
on the amount of force applied but also on the position of the point of application of the force relative to the axis
of rotation. By convention, the torque of a force that tends to cause a clockwise (CW) rotation (on a plane) is
negative while the torque that tends to cause a counterclockwise (CCW) rotation is positive.
where F = force
d = distance (measured on the perpendicular direction ) from the axis
of rotation to the line of action of the force.
Note that inanimate objects, such as table-tops and axles, can exert forces on objects resting on them.
Recognizing all forces applied to a given object is extremely important. Equally important is to know where, on
the object, these forces are applied.
For example, one of the forces that acts on a body is the force of gravity or weight F g = mg (its torque denoted
τ g ).
It is important to know where that force acts, i.e. to know the position of the centre of gravity, x cm .
PART I: DETERMINATION OF THE CENTRE OF
GRAVITY
MATERIAL:
Support frame, rod (ruler), pulley and weights.
PROCEDURE:
1. Measure the mass, m, of the rod (ruler).
2. Support the rod horizontally as in Fig. 1.
3. Measure the force F and the distance d.
4. Repeat steps 2-3 for two other values of d.
5. Fill in Table 1 and determine from the data the
location of the centre of gravity of the rod (ruler).
d
Pivot
Figure 1. Determination of the centre of
gravity
F
d (m) F (N) τ g (N.m)
Table 1. Determination of the centre of gravity

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PART II: EQUILIBRIUM WITH PARALLEL FORCES
MATERIAL:
Support frame, rod (ruler), pulley and weights.
PROCEDURE:
1. Place a mass M = 500 g a distance l along the
rod (ruler) from the pivot.
2. Support the rod horizontally, as in Fig. 2,
with the left end resting again on the pivot.
3. Measure the force F and the distance d that
yields static equilibrium.
4. Repeat step 2-3 for two other values of
M and l.
5. Fill in Table 2.
6. What is the force on the rod at the pivot?
7. Discuss your results.
F
d
Mg
l
Figure 2. Part II: Equilibrium with parallel forces
l (m) d (m) F (N) Fd (N.m) τ g =mg. x cm (Nm) Mgl (N.m) Σ τ i (N.m)
Table 2. Part II: Equilibrium with parallel forces
PART III: EQUILIBRIUM WITH PARALLEL FORCES
MATERIAL:
Support frame, rod (ruler), pulleys and weights.
PROCEDURE:
1. Start with a similar mass M = 500 g a distance
l along the rod from the pivot.
2. Support now the left end of the rod (ruler)
with a hanging weight P.
3. Adjust F and P to reach static equilibrium
(with the rod horizontal) and record the forces
F, Mg and P.
4. Repeat step 3 for two other values of
M and l.
5. Fill in Table 3.
P
F
Mg
Figure 3. Part III: Equilibrium with parallel forces
F (N) P (N) Mg (N) F g =mg (N)
Table 3. Part III: Equilibrium with parallel forces
6. Are all entries zero in the last column of Tables 2 and 3, as expected?
7. Discuss your results.
8. For comparable values of M and F, how does the value of P compare with the value found in step 6 of part
II?

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I. PRELAB QUESTIONS
1. What is meant by static equilibrium? [1]
2. How do you define the torque (or moment of a force)? Give the most general definition and illustrate
with a diagram. [1.5]
3. Can a body be in static equilibrium if subjected to only one force? Explain briefly. [1.5]
4. Define centre of gravity. [1]
The following instructions will help you prepare to write the report:
Read the procedure in each part of this experiment and make sure you understand the structure of the
three particular tables required to record the data.
II. PROCEDURE
1. Draw a diagram to describe the apparatus used to determine the centre of gravity of a bar.
2. Fill up the tables as required.
III. CONCLUSIONS
1. Is the centre of gravity where you expect if to be? Explain or justify the discrepancies.
2. Based on the theory of static equilibrium, which values do you expect to obtain for the last columns of
tables 2 and 3 and which values do you get for those cells? Explain the discrepancies.