When an object is at rest, it is in a state of equilibrium with no net force acting on it. This means the forces acting on the object are balanced. However, when an unbalanced or net external force acts on an object at rest, it disrupts this equilibrium and causes the object to accelerate in the direction of the net force. This acceleration results in a change in the object’s velocity and allows it to overcome inertia and begin moving.

## What is a force?

A force is a push or pull that acts on an object and changes its state of motion. Forces can vary greatly in magnitude and direction. According to Newton’s first law of motion, an object at rest will stay at rest and an object in motion will stay in motion unless acted upon by an unbalanced force.

Some examples of forces include:

– Friction: A force that resists the relative motion between two surfaces in contact. Acts to slow down moving objects.

– Tension: Force that acts through a rope, string, cable or wire when it is pulled tight by forces acting from each end.

– Normal force: Force exerted by a surface on an object to prevent it from sinking into the surface. Acts perpendicular to the surface.

– Gravity: Downward force exerted by earth’s mass that pulls objects toward it. Gravity gives weight to objects.

– Air resistance: Frictional force exerted by air pushing against a moving object. Tends to slow down objects moving through air.

– Applied force: External force applied to an object by direct contact, such as a person pushing or pulling it.

## Requirements for an unbalanced force

In order for an unbalanced or net force to act on an object at rest, two key requirements must be met:

### Requirement 1: The force must be external

The net force must come from outside the object rather than internal forces. When all the internal forces within an object are balanced, the object maintains its state of rest or constant velocity motion.

An external force is needed to disrupt this equilibrium. Some examples of external forces include gravity, magnetism, applied force from contact, air resistance, tension or friction from another object. Internal forces such as the structural forces holding an object together do not cause acceleration.

### Requirement 2: The force must be non-zero

If the external force equals zero, there is no net force on the object. A non-zero net external force is required to accelerate a stationary object. This means the vector sum of all external forces acting on the object cannot equal zero.

There must be an unbalance between the various forces acting horizontally and vertically on the object in order for any acceleration to take place. Even a small net external force will cause the object to accelerate.

## Effects of Unbalanced Force on an Object at Rest

When a non-zero net external force acts on an object at rest, two main effects are observed:

### Effect 1: The object accelerates

Newton’s second law of motion states that the net external force on an object is equal to its mass multiplied by its acceleration.

F_{net} = ma

Where:

F_{net} = net external force (N)

m = mass of object (kg)

a = acceleration (m/s^{2})

This means an unbalanced external force causes an object at rest to accelerate in the direction of the net force. The greater the net force, the greater the magnitude of acceleration produced.

### Effect 2: Work is done on the object

Work is done on an object when an applied force moves it through a displacement. Since the unbalanced force causes the stationary object to accelerate and move, it is doing work on the object.

Work = Force x Displacement

W = Fd

Where:

W = Work done by force (J)

F = Force applied (N)

d = Displacement of object (m)

The work done on the object by the unbalanced force results in a transfer of energy to the object. This energy goes into overcoming its inertia, causing it to accelerate from rest.

## Examples of Unbalanced Forces Causing Motion

### Pushing a box at rest

When a person exerts a push on a stationary box with their hands, this applied force acts horizontally on the box. As there are no other significant horizontal forces, the applied force is unbalanced. This results in the box accelerating in the direction it was pushed.

### Falling objects

When an object is held at rest above the ground and then released, the gravitational force acting downwards is unbalanced. This results in a downwards acceleration and the object starts falling vertically towards the ground.

### Magnet moving a paperclip

When a magnet is brought close to a stationary paperclip, the magnetic force exerted on the paperclip is unbalanced. This causes the paperclip to accelerate towards the magnet. The paperclip moves with increasing velocity until is sticks to the magnet.

### Static and kinetic friction

When a force is applied to an object at rest on a flat surface, static friction comes into play. As long as static friction is equal and opposite to the applied force, the object remains stationary. However, when the applied force exceeds the maximum possible static friction force, the object accelerates due to the unbalanced force. This unbalanced force then becomes the kinetic friction as the object slides across the surface.

## Analysis Methods for Unbalanced Force Problems

To analyze scenarios involving unbalanced forces on objects at rest, some useful methods include:

### Free body diagrams

Drawing a free body diagram isolates the object and shows all forces acting on it. This allows identification of any unbalanced force.

### Applying Newton’s laws of motion

Newton’s first and second laws can determine whether a net external force exists, and predict the motion that will result.

### Determining the net force quantitatively

All the forces are resolved into vertical and horizontal components using trigonometry. The components along each axis are summed to find the net force.

### Using force tables

Tabulating all the forces with their direction, magnitude and components clarifies which direction has an unbalanced force.

### Applying friction equations

The maximum static friction force can be calculated and compared to applied force to determine if motion will occur.

## How to Calculate the Acceleration from an Unbalanced Force

The acceleration of an object at rest produced by an unbalanced force can be calculated using:

### Step 1) Draw a free body diagram

Isolate the object and draw all external forces acting on it. Assign appropriate symbols.

### Step 2) Apply Newton’s 2nd law

F_{net} = ma

Where F_{net} is the vector sum of all external forces.

### Step 3) Calculate net force

Add vector components of all forces acting along the movement direction.

Or find the magnitude and direction of the resulting net force vector.

### Step 4) Determine mass of object

Obtain mass m in kg.

### Step 5) Calculate acceleration a

Divide net force by mass:

a = F_{net}/m

Acceleration direction is same as net force direction.

### Step 6) Plug in values and solve

Substitute the known values and calculate the acceleration of the object in m/s^{2}.

### Example Problem

For the object above with mass 2 kg:

F_{net} = F_{app} – F_{friction}

= 18 N – 6 N

= 12 N

a = F_{net}/m = 12 N/2 kg = 6 m/s^{2}

Therefore, with an unbalanced force of 12 N, the object’s acceleration is 6 m/s^{2}.

## Effects of Varying Force Magnitude

According to Newton’s second law, doubling the net force on an object at rest doubles its acceleration. Some general effects of increasing unbalanced force magnitude:

– Greater net force causes greater acceleration

– Heavier objects accelerate slower from the same force

– Net force directly proportional to mass x acceleration

– For a given mass, larger force decreases time to reach a velocity

– Force is a vector so direction affects motion produced

This relationship allows predicting motion based on the force magnitude and direction.

### Table showing effect of different net forces on a 5 kg object initially at rest:

Net Force (N) | Acceleration (m/s^{2}) |
Time to reach 10 m/s (s) |
---|---|---|

10 | 2 | 5 |

20 | 4 | 2.5 |

30 | 6 | 1.67 |

40 | 8 | 1.25 |

## Factors Opposing the Unbalanced Force

While an unbalanced force causes an object at rest to accelerate, there are some factors that hinder this motion by opposing the external net force:

### Friction

Frictional forces between an object and the surface it rests on creates resistance to the applied force. Static friction initially holds the object in place until exceeding the maximum static friction force. Kinetic friction then slows down its motion.

### Air resistance

The frictional drag force exerted by air pushes against objects moving through the air. Air resistance tends to decrease acceleration from an applied force.

### Tension

Forces transmitted through cables, ropes and strings act in the opposite direction of an applied force. The tension provides resistance to motion.

### Inertia

This resistance to change in motion makes it harder to accelerate stationary objects. More force is required to overcome inertia and accelerate larger mass objects.

### Deformation

If the applied force deforms an object, some energy is absorbed in deforming rather than accelerating it. This decreases the acceleration produced.

By accounting for these factors impeding the unbalanced force, more accurate motion prediction is possible. Minimizing these opposing forces allows the object to accelerate faster.

## Practical Applications

Understanding the effect of unbalanced forces has useful applications in:

### Transportation

Calculating friction and air resistance allows vehicle design for faster acceleration. Aerodynamic design minimizes drag.

### Sports

The motion of athletes and sports projectiles considers unbalanced forces and oppositional factors. This improves performance.

### Engineering

Engineers analyze unbalanced force effects when designing moving structures and mechanisms to improve functionality.

### Physics experiments

Measuring the acceleration of objects from known unbalanced forces allows determination of their mass and verification of physics theories.

### Amusement park rides

The motions of rollercoasters involve unbalanced forces. Ride designs apply physics concepts for safety and thrill factor.

## Conclusion

An unbalanced external force applied to an object at rest overcomes inertia and produces acceleration in the direction of the net force. This disrupts the object’s equilibrium and imparts motion. Greater net force causes greater magnitude of acceleration, with various factors like friction reducing the realized motion. Understanding the precise effects of unbalanced forces allows predicting and controlling an object’s motion. This has important use across science, sports and engineering.