Equilibrium of forces
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State the principle of moments.
The principle of moments states that for an object in equilibrium, the sum of the clockwise moments about a point is equal to the sum of the anticlockwise moments about the same point. This implies no net rotational effect.
What two conditions must be met for an object to be in complete equilibrium?
For complete equilibrium, there must be no resultant force (translational equilibrium) and no resultant torque (rotational equilibrium). This means the vector sum of all forces is zero, and the sum of moments about any point is zero.
Describe how a vector triangle can be used to represent three coplanar forces in equilibrium.
When three coplanar forces are in equilibrium, they can be represented by the sides of a closed triangle. The arrows representing the forces should follow head to tail, illustrating that their vector sum is zero.
A beam is supported at two points. How do you determine the reaction forces at the supports when a load is placed on the beam?
Apply the principle of moments by taking moments about one of the supports. This allows you to calculate the reaction force at the other support. Then, use the condition that the sum of upward forces equals the sum of downward forces to find the remaining reaction force.
Explain the difference between 'centre of gravity' and 'centre of mass'.
The centre of gravity is the point where the entire weight of the object appears to act. The centre of mass is the point where the entire mass of the object appears to be concentrated. They are usually the same, but differ when gravity is non-uniform.
How does increasing the base area of an object affect its stability?
Increasing the base area of an object increases its stability. A larger base area means the centre of gravity can be displaced further before the line of action of the weight falls outside the base, causing the object to topple.
Describe the effect on equilibrium if the lines of action of all forces acting on a body pass through a single point.
If the lines of action of all forces pass through a single point, there is no net torque about that point. The body is in translational equilibrium if the vector sum of the forces is also zero, but may still rotate if an external torque is applied.
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