When an object is at rest, this means it is not moving or accelerating. The forces acting on the object must be balanced in order for it to remain at rest. This is explained by Newton’s first law of motion, also known as the law of inertia, which states that an object at rest will stay at rest unless acted upon by an unbalanced force.
Forces Must Be Equal and Opposite
For an object to be at rest, the forces acting on it must be equal in magnitude and opposite in direction. This results in the forces cancelling each other out so that the net force on the object is zero. Some examples of balanced forces keeping an object at rest include:
Normal Force and Gravity
A book resting on a table experiences two vertical forces – the downward pull of gravity and the upward push of the normal force from the table. These two forces are equal in size but opposite in direction. This results in zero net force vertically, so the book remains at rest.
Tension and Friction
A block tied to a string and resting on a rough surface experiences tension in the string and friction from the surface. As long as these two horizontal forces are equal and opposite, the block will not accelerate.
Applied Force and Friction
Pushing a box at constant velocity across a floor requires balancing the applied force with the kinetic frictional force. As long as these forces are balanced, the velocity of the box will remain unchanged.
No Acceleration
Newton’s second law of motion states that the net force on an object is equal to its mass multiplied by its acceleration.
Fnet = ma
Since the net force on an object at rest is zero, the acceleration must also be zero. With no net force, there is no acceleration according to Newton’s second law. Therefore, an object at rest will remain at rest.
Examples of a Balanced Force System
There are many common examples of objects remaining at rest due to balanced forces:
Books on a Table
As described earlier, a book resting on a table experiences equal and opposite normal and gravitational forces. This keeps the book at rest.
Blocks on an Incline
A block may rest on an inclined plane if friction is sufficient to balance the component of weight parallel to the surface. This frictional force prevents motion down the plane.
Skyscrapers
Extremely tall skyscrapers require large compressive forces at their base to balance the gravitational forces trying to make the building collapse. Proper engineering ensures these forces are balanced.
Dams
Dams are designed so that the compressive strength along the dam wall balances the force exerted by the water pushing against the upstream side.
Equilibrium Condition
The condition where the net external force and torque acting on a rigid object are zero is known as equilibrium. For an object at rest, the following must be true:
- The net external force is zero (balanced forces)
- The net external torque is zero (balanced torques)
With no net force or torque, an object at equilibrium will remain at rest or continue moving at a constant velocity. This is a stable equilibrium.
Breaking Equilibrium
If an additional external force or torque is applied to an object at rest, the equilibrium condition is broken. This results in a net force and acceleration according to Newton’s second law.
Some ways equilibrium can be broken include:
- Pushing or pulling on the object
- Applying an unbalanced torque by turning a force
- Removing a force (e.g. table taken away from a book)
- Changing the coefficient of friction
- Applying components of force not along the lines of action
The object will then accelerate in the direction of the net force until a new equilibrium condition is reached.
Special Case: Static Equilibrium
Static equilibrium is a special case of equilibrium where both the net external force and torque are zero, and the object remains at rest.
This occurs when:
- All forces balance in all directions (Fx = 0, Fy = 0, Fz = 0)
- All torques balance about any axis (τx = 0, τy = 0, τz = 0)
Some examples of static equilibrium include a book on a table, a car stopped at a traffic light, or a bridge with no moving loads. Small disturbances may occur, but the object remains at rest in general.
Solving Statics Problems
Analyzing static equilibrium situations often involves:
- Drawing a free body diagram showing all forces acting on the object
- Applying Newton’s first law – net F = 0 and net τ = 0
- Resolving vectors into x and y components
- Summing forces in each direction (ΣFx = 0, ΣFy = 0)
- Taking moments about any point (ΣMo = 0)
- Solving the equations algebraically
This provides enough equations to solve for all unknown quantities like forces, torques, and pressures.
Example Statics Problem
For the beam shown above in static equilibrium:
- Taking moments about A yields (100)(2) – (20)(6) – (Fy)(4) = 0
- Fy = 60 N
Summing forces in the y-direction:
- ΣFy = 0 = 100 – 20 – 60
- Therefore, the upward force Ay must be Ay = 180 N
Impact on Structural Design
Understanding static equilibrium is crucial for structural design in architecture and engineering. Designing buildings, bridges, machines, and components involves ensuring stability by properly balancing all anticipated forces and loads.
Some key considerations include:
- Calculating expected loads like dead loads, live loads, wind loads
- Distributing loads safely to foundations
- Selecting appropriate materials and shapes to handle stresses
- Using compressive, tensile, and diagonal members as needed
- Avoiding buckling or fracture by managing component stability and strength
Proper static equilibrium analysis prevents collapse and allows the structure to remain at rest, only moving within the elastic range without permanent deformation. This is essential to safety and functionality.
Conclusion
When an object is at rest, this means the net external force and torque acting on it are zero. The forces are balanced such that the object remains in equilibrium. Without any net force, the acceleration is zero according to Newton’s second law. At equilibrium, the object will remain stationary or move at constant velocity unless disturbed. Understanding these principles helps explain everyday situations and has important implications in engineering design. Proper analysis of static equilibrium ensures structures can withstand expected loads and remain safe.