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Force and Motion

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Force and Motion

Why does a football fly through the air when being kicked? It's because the foot exerts a force on the football! Forces determine how objects move. Therefore, to make calculations and predictions about the trajectory of any object we need to understand the relationship between forces and motion. Sir Isaac Newton noticed this and came up with three laws that summarize the effects that force has on the motion of an object. That is right; with only three laws, we can describe all motion. Their accuracy is so good that this was enough to calculate the trajectories and interactions that allow us to walk on the moon! The first law explains why objects cannot move on their own. The second is used to calculate the motion of projectiles and vehicles. The third one explains why guns recoil after shooting and why the combustion with the expelling of gasses results in an upward thrust for a rocket. Let's go through these laws of motion in detail and explore how they can be used to explain the world we see around us by looking at some real-life examples.

Forces and motion: Definition

In order to develop a good understanding of how forces and motion are related, we will need to get familiar with some terminology, so let's start by explaining what we refer to as motion and force in more detail.

We say that an object is in motion if it is moving. If it is not moving, we say that it is in repose.

The specific value of the velocity at a given time defines the state of motion of an object.

Force is any influence that can cause a change in the state of motion of an object.

A force can be thought of as a push or pull that acts on an object.

Forces and motion properties

It is very important to keep in mind that velocity and forces are vectors. This means that we need to specify their magnitude and direction to define them.

Let's consider an example where we can see the importance of the vector nature of velocity to talk about the state of motion of an object.

A car is heading west at a constant speed of. After an hour, it turns and continues at the same speed, heading north.

The car is always in motion. However, its state of motion changes even if its speed remains the same the whole time because, at first, it is moving to the west, but it ends up moving to the north.

A force is also a vector quantity, so it doesn't make sense to talk about forces and motion if we do not specify its direction and magnitude. But before going into this in more detail, let's talk about units of force. The SI units of force are newtons. One newton can be defined as a force that produces an acceleration of one meter per second squared in an object with a mass of one kilogram.

Forces are usually represented by the symbol. We can have many forces acting on the same object, so next, we will talk about the basics of dealing with multiple forces.

Force and motion basics

As we will see later, forces determine the motion of objects. Therefore, to predict the motion of an object, it is very important to know how to deal with multiple forces. Since forces are vector quantities, they can be added together by adding their magnitudes based on their directions. The sum of a group of forces is called the resultant or net force.

The resultant force or net force is a single force that has the same effect on an object as two or more independent forces acting on it.

Force and Motion Force diagram showing the resultant force StudySmarterTo calculate the resultant force, all the forces acting on an object must be added as vectors, StudySmarter Originals

Have a look at the above image. If two forces act in opposite directions, then the resultant force vector will be the difference between them, acting in the direction of the force with greater magnitude. Conversely, if two forces act in the same direction, we can add their magnitudes to find a resultant force that acts in the same direction as them. In the case of the red box, the resultant force istowards the right. On the other hand, for the blue box, the resultant istowards the right.

While talking about sums of forces, it is a good idea to introduce what unbalanced and balanced forces are.

If the resultant of all the forces acting on an object is zero, then they are called balanced forces and we say that the object is in equilibrium.

As the forces cancel each other, this is equivalent to having no force acting on the object at all.

If the resultant is not equal to zero, we have an unbalanced force.

You will see why it is important to make this distinction in the later sections. Now let's continue by looking at the relation between forces and motion through Newton's laws.

Relationship between forces and motion: Newton's Laws of Motion

We mentioned previously, that forces can change the state of motion of an object, but we haven't said exactly how this happens. Sir Isaac Newton formulated three fundamental laws of motion that describe the relationship between the motion of an object and the forces acting on it.

Newton's first law of motion: Law of inertia

Newton's First Law

An object continues to be in a state of rest or move with uniform velocity until an external unbalanced force acts on it.

This is closely related to an inherent property of every object with mass, called inertia.

The tendency of an object to keep moving or preserve its state of rest is called inertia.

Let us look at an example of Newton's First Law in a real-life.

Force and motion people tending to move after a car stops suddenly StudySmarter Inertia causes you to keep moving when a car suddenly stops, Buy Your Auto Insurance

Imagine that you're a passenger in a car. The car is moving in a straight line when, suddenly, the driver makes an abrupt stop. You get thrown forward even if nothing pushes you! This is the inertia of your body resisting a change to its state of motion, trying to keep moving forward in a straight line. According to Newton's first law, your body tends to maintain its state of motion and resist to the change - slowing down - imposed by the braking car. Luckily, wearing a seat belt can stop you from being thrown forward abruptly in the case of such an event!

But what about an object originally at rest? What can this inertia principle tell us in that case? Let us look at another example.

Force and Motion a football at rest StudySmarterThe football remains at rest because no unbalanced force is acting on it, StudySmarter Originals

Look at the football in the above image. The ball remains at rest as long as there is no external force acting on it. However, if someone exerts force by kicking it, the ball changes its state of motion - stops being at rest - and begins to move.

Force and Motion A foot exerting force on a football while kicking it StudySmarterWhen the ball is kicked, a force acts on it for a short time. This unbalanced force makes the ball leave the rest, and after the force is applied, the ball tends to continue moving with constant velocity. StudySmarter Originals

But wait, the law also says that the ball will continue to move unless a force stops it. However, we see that a moving ball eventually comes to rest after being kicked. Is this a contradiction? No, this happens because there are multiple forces such as air resistance and friction that act against the motion of the ball. These forces ultimately cause it to stop. In the absence of these forces, the ball will continue to move with constant velocity.

From the above example, we see that an unbalanced force is necessary to produce motion or change it. Keep in mind that balanced forces are equivalent to having no force acting at all! It doesn't how many forces are acting. If they are balanced, they won't affect the state of motion of the system. But how exactly does an unbalanced force affect the motion of an object? Can we measure this? Well, Newton's second law of motion is all about this.

Newton's second law of motion: Law of mass and acceleration

Newton's Second Law

The acceleration produced in an object is directly proportional to the force acting on it and inversely proportional to the mass of the object.

Force and Motion Diagram of people pulling on a mass on a cart StudySmarterThe acceleration caused by a force is directly proportional to the force but inversely proportional to the mass of the object. Theory Labster

The above image illustrates Newton's Second Law. Since acceleration produced is directly proportional to the force applied, doubling the force applied to the same mass causes the acceleration to double as well, as shown in (b). On the other hand, since acceleration is also inversely proportional to the mass of the object, doubling the mass while applying the same force causes the acceleration to be reduced by half, as shown in (c).

Remember that velocity is a vector quantity that has a magnitude - speed - and a direction. Since acceleration occurs whenever velocity changes, a force producing an acceleration on an object can:

  • Change both the speed and direction of the motion. For example, a baseball hit by a bat changes its speed and direction.
  • Change the speed while the direction remains constant. For example, a car braking keeps moving in the same direction but slower.

  • Change the direction while the speed remains constant. For example, the earth moves around the sun in a motion that can be considered circular. While it is moving at approximately the same speed, its direction is constantly changing. This is because it is subject to the gravitational force of the sun. The following pictures show this using a green arrow to represent the earth's velocity.

Force and Motion earth moving around the sun StudySmarterEarth moves approximately at the same speed, but its direction constantly changes due to the sun's gravitational force, describing an approximately circular path. StudySmarter Originals

Force and motion formula

Newton's second law can be mathematically represented as follows:

Note that if multiple forces are acting on the body, we have to add them to find the resultant force and then the acceleration of the object.

Newton's second law is also very often written as. This equation states that the net force acting on a body is the product of its mass and acceleration. The acceleration will be in the direction of the force that is acting on the body. We can see that the mass appearing in the equation determines how much force is needed to cause certain acceleration. In other words, the mass tells us how easy or difficult it is to accelerate an object. Since inertia is the property of a body resisting a change in its motion, mass is related to inertia, and it is somehow a measure of it. This is why the mass appearing in the equation is known as inertial mass.

Inertial mass quantifies how difficult it is to accelerate an object and it is defined as the ratio of the applied force applied to the produced acceleration.

We are now ready for the final Law of Motion.

Newton's Third Law of Motion: Law of action and reaction

Newton's Third Law of Motion

Every action has an equal and opposite reaction. When one body exerts a force on another (action force), the second body responds by exerting an equivalent force in the opposite direction (reaction force).

Note that the action and reaction forces are always acting on different bodies.

Force and motion action and reaction force of a hammer and a nail StudySmarterBy Newton's third law, when a hammer hits a nail, the hammer exerts a force over the nail but the nail also exerts an equal force on the hammer in the opposite direction. StudySmarter

Consider a carpenter hammering a nail into a floorboard. Let's say that hammer is being driven with a force of magnitude. Let us consider this as the action force. For the small interval that the hammer and the nail are in contact, the nail responds by exerting an equal and opposite reaction forceon the head of the hammer.

What about the interaction between the nail and the floorboard? You guessed it! When the nail strikes, exerting a force on the floorboard, the floorboard exerts a reaction force on the tip of the nail. Therefore, when considering the system nail-floorboard, the action force is exerted by the nail and the reaction by the floorboard.

Force and motion examples

We have already seen some examples showing how force and motion are related while introducing Newton's laws. In this last section, we will see some examples of force and motion in everyday life.

It is very intuitive to think that something in repose will keep in repose unless a force acts on it. But remember that Newton's First Law also says that an object in motion remains in the same state of motion - same speed and same direction - unless a force changes this. Consider an asteroid moving through space. Since there is no air to stop it, it continues moving at the same speed and in the same direction.

Force and Motion asteroid moving through space StudySmarterAn asteroid moves with constant velocity (green arrow) in space as there is no unbalanced force acting on it. StudySmarter Originals

And as mentioned at the beginning of the article, a rocket is a great example of Newton's third law, where the expelled gases have a reaction force on the rocket, producing a thrust.

Force and Motion a rocket expelling gases StudySmarterThe gases expelled by the rocket and the thrust are an example of an action-reaction pair of forces. StudySmarter Originals

Let's look at a final example and try to identify all the laws of motion that are applicable to the situation.

Consider a book lying on a table. Which laws of motion do you think are being applied here? Let's go through all of them together. Even though the book is at rest, there are two forces at play.

  1. The weight of the book pulls it down against the table.
  2. By Newton's third law, there is a reaction from the table to this weight, acting on the book. This is called the normal force.

Force and Motion diagram of forces for a book on a table StudySmarterThe table responds to the weight of the book pressing against it by exerting a normal force, StudySmarter Originals

When an object interacts with another by making contact with it, the second object generates a reaction force perpendicular to its surface. These forces, perpendicular to the interacting objects' surfaces, are called normal forces.

Normal forces are called that way not because they are 'common' but because 'normal' is another way to say perpendicular in geometry.

Returning to our example, since the forces acting on the book are balanced, the resultant force is zero. This is why the book remains at rest, and there is no motion. If now, an external force pushed the book to the right, according to Newton's Second Law, it would accelerate in this direction because this new force is unbalanced.

Force and Motion diagram of forces for a book on a table StudySmarterThe book remains at rest because no unbalanced force is acting on it, StudySmarter Originals

Force and Motion - Key takeaways

  • A force can be defined as a push or pull that acts on an object.
  • Force is a vector quantity. Thus it is defined by specifying its magnitude and direction.
  • The resultant or net force is a single force that has the same effect that two or more independent forces would have when acting together on the same object.
  • Newton's first law of motion is also called the law of inertia. It states that an object continues to be in a state of rest or move with uniform velocity until an external unbalanced force acts on it.
  • The tendency of an object to keep moving or preserve its state of rest is called inertia.
  • Newton's second law of motion states that the acceleration produced in a moving object is directly proportional to the force acting on it and inversely proportional to the mass of the object.
  • Inertial mass is a quantitative measure of the inertia of an object and can be calculated as the ratio of the applied force to the acceleration of an object,.
  • Newton's third law of motion states that every action has an equal and opposite reaction.

Frequently Asked Questions about Force and Motion

An object in motion is that which is moving. And its velocity value defines its state of motion. 


A force is defined as any influence that can produce a change in the speed or direction of the motion of an object. We can also define a force as a push or pull. 

Force can change the state of motion of a system. This is described in Newton's laws of motion. 


Newton's first law of motion, states that an object continues to be in a state of rest or move with a constant velocity until an external unbalanced force acts on it. If an unbalanced force acts over a body, Newton's second law tells us that it will be accelerated in the direction of the applied force.

Newton's second law can be represented by the formula F=ma. This allows us to calculate the force required to produce a specific acceleration on a body of known mass. On the other hand, if the force and the mass are known we can calculate the acceleration of the object and describe its motion. 

Circular motion is the movement of a body along the circumference of a circle. Circular motion is only possible when an unbalanced force acts on the body, acting towards the centre of the circle. This force is called centripetal force.

  • A book lying on a table shows how an object keeps its state of motion when no net force acts on it - Newton's Frist Law.
  • A car slowing down after braking shows how a force changes the state of motion of a system - Newton's Second Law.
  • The recoil of a gun firing a bullet shows that as a force is exerted on the bullet, this reacts exerting a force of the same magnitude but in opposite direction on the gun - Newton's Thirf Law.

Final Force and Motion Quiz

Question

Velocity is a scalar quantity.

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Answer

False

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Question

Velocity has both magnitude and ...

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Answer

Direction

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Question

Acceleration is a vector quantity. 

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Answer

True

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Acceleration can be determined from a velocity-time graph, it is equal to the graphs...

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Area

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The change in velocity can be obtained from an acceleration-time graph by calculating the...

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Answer

Area under the curve

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An object traveling in a circle will have a changing velocity due to ...

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Changing speed 

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What does a steep line correspond to in a velocity-time graph?


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High acceleration

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Difference between velocity and speed?


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Velocity has both magnitude and direction whereas speed only has magnitude.

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What is the vertical axis in a velocity-time graph?


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Answer

velocity

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Question

What does a straight line parallel to the x-axis correspond to in a speed-time graph?


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No acceleration

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Speed is a vector quantity.

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False

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Distance is a ...

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Scalar quantity

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The SI unit for speed is ...

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m/s

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What is the equation for speed?

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Distance/Time

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What is the speed triangle used for?

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Answer

The Speed triangle is an easy way to remember the relationship between speed, distance, and time.

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Why is speed a scalar quantity?

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Answer

It has only magnitude

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Question

 Mr. Andrew drives his motorbike for 3 hrs at 150 miles/hr. How far will he travel?


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450 miles

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Who formulated the Laws of motion?

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Sir Issac Newton

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The First Law of motion is also called the ...

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Law of inertia.

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Why do we need to wear seat belts?

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Because of the inertia of our body, we tend to keep moving forward when the vehicle stops suddenly. This can be dangerous, especially during sudden and extreme braking. We could collide with the interior of the car and cause serious injuries. A seatbelt prevents this from happening by keeping us fastened to the seat.

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Question

Which Newton's Law of motion explains why a book lying on the table remains at rest?

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Answer

First Law of motion.

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Which Newton's Law of motion explains why we need to wear seat belts while driving?

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Answer

First Law of motion.

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An object of greater mass requires a greater force to acquire the same acceleration than a lighter body. Which Newton's Law explains this?

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Newton's Second Law.

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What is inertia?

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A property of matter to resist a change in its state of motion.

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A magician pulling a tablecloth from underneath some dishes without disturbing them is explained by ...

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Newton's First Law.

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Why do you lean towards the opposite side when a car turns?

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Because of inertia, our body tends to keep moving in a straight line.

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Acceleration is directly proportional to ...

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Force.

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Forces always act in equal and opposite pairs.

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True.

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A rocket flying due to the propulsion of rocket fuel is explained by ...

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Newton's Third Law.

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What is Newton's First Law?

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Newton's First Law of motion, also called the Law of inertia, states that an object remains in the same state of motion until an unbalanced force acts on it. This means that the object either continues to be at rest or moving with uniform velocity.  

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What is Newton's Second Law?

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Newton's Second Law of motion, also called the Law of mass and acceleration, states that the acceleration of an object is directly proportional to the force acting on it and inversely proportional to the object's mass.

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What is Newton's Third Law?

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Newton's Third Law of motion, also called the Law of action and reaction, states that every action has an equal and opposite reaction. Therefore, when one body exerts a force on another (action force), the second body responds by exerting an equivalent force in the opposite direction (reaction force)


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When is it most helpful to use motion graphs?

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When an object has uniform motion.

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Which one of these is not a vector?

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Distance.

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On a distance-time graph, what would a horizontal line mean?

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The object is stationary.

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What does the gradient of a distance-time graph tell us about an object's motion?

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Velocity.

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What can you determine by calculating the area under a velocity-time graph?

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Displacement.

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On a velocity-time graph, does a steeper gradient mean an acceleration of greater or less magnitude?

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Greater.

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What can you determine by calculating the area under an acceleration-time graph?

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The change in velocity.

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What does the gradient of a velocity-time graph tell us about an object's motion?

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Acceleration.

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What does the gradient of an acceleration-time graph tell us about an object's motion?

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Jerk.

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On a velocity-time graph, what does it mean when the line crosses the x-axis?

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The object has reversed direction.

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On an acceleration-time graph, what does it mean when the line crosses the x-axis?

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The object begins to slow down if crossing from positive to negative acceleration.


The object begins to speed up if crossing from negative to positive acceleration.

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Write a definition of uniform motion using only one sentence.

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If an object is travelling with uniform motion, it is moving in a straight line at a constant speed.

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What is the value of acceleration due to gravity at the surface of the Earth?

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9.8 m/s2.

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On a displacement-time graph, is it possible to read the distance travelled by the object over time as well as displacement?

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Yes.

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Question

What are the two qualitative demands for a force to be an impact force?

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It causes a very large acceleration and has a very small duration.

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If an object has a kinetic energy of 250 J and collides with a wall such that it suddenly stops moving, what is the work done on the object?

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The difference in kinetic energy is 250 J, so the work done on the object is 250 J.

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How do you calculate impact force from change in kinetic energy E and distance s over which the force acts?

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E/s

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How do you calculate the duration of the impact from the initial speed v of the object and the distance s over which the force acts?

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2s/v

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