The facts:
1. The main properties of a given force
are:
the point of application,
-the magnitude,
- the line of action and
-the sense.
Let us refer to these properties that are usually confused or vaguely understood. These are the point of application and the line of action.
the point of application,
-the magnitude,
- the line of action and
-the sense.
Let us refer to these properties that are usually confused or vaguely understood. These are the point of application and the line of action.
The point of
application is the exact location at which a force is applied to a body.
A force can be seen as a segment of an indefinitely long
line. To each force is associated a characteristic line, which is referred to
as its line of action.
2. A contact force is a force that acts at
the point of contact between two objects. In the figure the ground reaction
force which is analysed to its components R and F, is a contact force.
If there is no contact, there is no such a force. Since the magnitude of F (friction) is proportional to R, we say that when an object looses contact with the ground N=0 (and thus F=0)
Hint: when we are asked to find a condition so as an object does
not tip over, we start stating that N≥0 and then we apply the conditions for equilibrium.
By working these equations out, we make R the subject and then we demand N to
be non negative.
3. Conditions for equilibrium
·
An object
is in translational equilibrium when the sum of all the forces acting on the object equals zero.
In translational equilibrium, an object is either not moving, or moving at a constant velocity.
An object is in rotational equilibrium when the sum of all the external torques (moments) acting on it equals zero. In rotational equilibrium, an object either will not be moving, or moving at a constant angular velocity
In translational equilibrium, an object is either not moving, or moving at a constant velocity.
An object is in rotational equilibrium when the sum of all the external torques (moments) acting on it equals zero. In rotational equilibrium, an object either will not be moving, or moving at a constant angular velocity
4. Moment or torque of a force is a measure of that force's tendency
to cause a rotational acceleration in the same way that a force causes a linear
acceleration. In its simplest form, where a force of magnitude F is
acting a perpendicular distance d from the point of rotation, the
torque about that point is given by: τ=Fd
Example
A man is standing on a board which
has length L=4m and weight W1=150N. The board is supported at points A and B on
two trestles. The distance between these points is 2d=2m. The man weights w2=700N.
Calculate the maximum distance from the centre of the board at which the man
can stand without the board tips over.
In order to apply the condition for rotational equilibrium we
took the moments about B:
By applying the condition for translational equilibrium we
have
Since we don’t want the board to tip over:
Challenge
hints:
To start off apply the condition for rotational equilibrium taking
the moments around G
Then we resolve forces to their components perpendicular and parallel to the plane (advice the provided figure)
Then we try to solve the above formed equations with respect
of N1 and N2.
We claim that in order to avoid tipping over N1≥0 and N2≥0
Very useful will be the compound angles formulas.
Very useful will be the compound angles formulas.
We have to demonstrate good algebraic skills to reach to the desired
result.
Good luck.
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