U3AOS1 Topic 2: Forces

Forces are fundamental concepts in physics that describe the interactions which change the motion of objects. They play a crucial role in our understanding of the natural world and underlie the principles governing everything from the movement of celestial bodies to the behavior of everyday objects. This essay delves into the definition of forces, their types, and their significance in various contexts.

In physics, a force is defined as an interaction that causes a change in the motion of an object. It is a vector quantity, meaning it has both magnitude and direction. Forces can cause an object to accelerate, decelerate, change direction, or change shape. The unit of force in the International System of Units (SI) is the Newton (N), named after Sir Isaac Newton, who formulated the laws of motion that describe the behavior of forces.


Forces are vectors which have a direction and magnitude. They are represented through arrows where the size of the arrow is relative of the magnitude of force. In other words, big arrow means big force, small arrow means small force.

If there are multiple forces acting on an object you find the final force but adding all the forces up from tip to tail.




Use the simulation below to see how this works


Created with GeoGebra®, by Tan Seng Kwang, Link


Types of Forces

Forces can be categorized into several types based on their nature and the manner in which they act:

  1. Gravitational Force: This is the attractive force between two masses. It is described by Newton’s Law of Universal Gravitation, which states that every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. For example, the Earth’s gravitational pull keeps us anchored to its surface and governs the orbits of planets around the sun.


  2. Electromagnetic Force: This force acts between electrically charged particles. It includes both electric forces (between stationary charges) and magnetic forces (between moving charges). The electromagnetic force is responsible for the behavior of atoms and molecules, thus determining the structure of matter and influencing chemical reactions. This force can be attractive or repulsive, depending on the charges involved.


  3. Strong Nuclear Force: This is the force that holds the nuclei of atoms together. It acts over very short distances, approximately the size of an atomic nucleus, and is much stronger than the electromagnetic force. The strong nuclear force binds protons and neutrons in the nucleus, overcoming the electromagnetic repulsion between positively charged protons.


  4. Weak Nuclear Force: This force is responsible for certain types of radioactive decay and nuclear reactions, such as beta decay. It acts over short distances and is weaker than the strong nuclear force but stronger than gravity at the atomic level.


  5. Frictional Force: This force opposes the relative motion of surfaces in contact. It can be categorized into static friction (preventing motion between stationary objects) and kinetic friction (opposing motion between moving objects). Friction is crucial in everyday life as it enables us to walk, drive, and handle objects effectively.


  6. Normal Force: This is the support force exerted by a surface perpendicular to the object in contact with it. For instance, when an object rests on a table, the table exerts an upward normal force that balances the downward gravitational force on the object.


  7. Tension Force: This force is transmitted through a string, rope, or cable when it is pulled tight by forces acting from opposite ends. It acts along the length of the string or rope and is directed away from the object.


  8. Applied Force: This is the force exerted on an object by an external agent. For example, when you push a door open, the force you apply to the door is an applied force.


  9. Spring Force: This force is exerted by a compressed or stretched spring, described by Hooke’s Law. It states that the force exerted by a spring is proportional to its displacement from the equilibrium position, given by F=−kxF = -kx, where kk is the spring constant and xx is the displacement.


There are 3 laws of motion called Newton's Laws.


Newton's First Law: Law of Inertia

An object in will remain at rest or in constant motion (non-accelerating) until a force is applied to it.

An example of this is in space. If you are floating in space you will float in that direction forever unless a force is applied to you.


Newton's Second Law: F = ma

The Net Force (final force) a mass carries is dependent on its mass and acceleration.

\[ \displaystyle \Large \sum F= F_{\text{net}} = ma \]

ΣF=Fnet=ma\Sigma F = F_{net} = ma

Newton's Third Law: Law of Action and Reaction

For every action force there is an equal and opposite reaction force.


The force due to gravity is dependent on the mass of the being attracted and the gravitational field strength. This is denoted by

\[ \displaystyle \Large F_{g} = mg \]

Fg=mg

There is also a normal force which is the reaction force between objects that keep them in contact. Generally, \(F_{N}= F_{g} \) FN=Fg    however you will see in the coming chapters where that is not the case.

Example 1
A 5 kg object is subjected to a force of 20 N. What is the acceleration of the object?

Using Newton’s Second Law, F=maF = ma, where:

  • FF is the force (20 N),
  • mm is the mass (5 kg),
  • aa is the acceleration.

Rearrange to solve for acceleration aa: a=Fm=20 N5 kg=4 m/s2.a = \frac{F}{m} = \frac{20\ \text{N}}{5\ \text{kg}} = 4\ \text{m/s}^2.

So, the acceleration is 4 m/s24\ \text{m/s}^2.

Example 2
Calculate the gravitational force between two masses of 10 kg and 15 kg separated by a distance of 2 meters. (Use G=6.674×10−11 N m2/kg2G = 6.674 \times 10^{-11}\ \text{N m}^2/\text{kg}^2.)

Using Newton's Law of Universal Gravitation: F=Gm1m2r2F = G \frac{m_1 m_2}{r^2} where:

  • GG is the gravitational constant,
  • m1=10 kgm_1 = 10\ \text{kg},
  • m2=15 kgm_2 = 15\ \text{kg},
  • r=2 mr = 2\ \text{m}.

Calculate: F=(6.674×10−11)10×1522=(6.674×10−11)1504=(6.674×10−11)×37.5=2.501×10−9 N.F = (6.674 \times 10^{-11}) \frac{10 \times 15}{2^2} = (6.674 \times 10^{-11}) \frac{150}{4} = (6.674 \times 10^{-11}) \times 37.5 = 2.501 \times 10^{-9}\ \text{N}.

The gravitational force is 2.501×10−9 N2.501 \times 10^{-9}\ \text{N}.

Example 3
A 3 kg object hangs from a rope. What is the tension in the rope if the object is at rest?

When the object is at rest, the tension TT in the rope equals the weight of the object. Weight WW is given by: W=mgW = mg where g=9.8 m/s2g = 9.8\ \text{m/s}^2 (acceleration due to gravity).

Calculate:

T=W=mg=3 kg×9.8 m/s2=29.4 N.T = W = mg = 3\ \text{kg} \times 9.8\ \text{m/s}^2 = 29.4\ \text{N}.

So, the tension in the rope is 29.4 N29.4\ \text{N}.

Exercise &&1&& (&&1&& Question)

A box with a mass of 12 kg is being pulled across a horizontal surface with a coefficient of kinetic friction of 0.3. Calculate the frictional force if the pulling force is 50 N.

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Exercise &&2&& (&&1&& Question)

A car with a mass of 1000 kg needs to overcome a frictional force of 8000 N. What force must the car's engine provide to maintain constant speed?

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Exercise &&3&& (&&1&& Question)

Calculate the force of gravity on a 70 kg person on the Moon, where the acceleration due to gravity is 1.6 m/s21.6\ \text{m/s}^2.

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