GCSE Physics - Vector Diagrams and Resultant Forces #43

Summary

This educational video demonstrates the use of scale drawings to calculate resultant forces on objects. It illustrates how to combine forces acting in different directions, such as a cyclist pushing north with a force of 4 newtons while a wind blows east with 3 newtons, resulting in a 5 newton force at 37 degrees. The video also covers the concept of equilibrium when forces balance out and the process of resolving vectors, as shown by breaking down a 50 newton force into its horizontal and vertical components on a ramp. The clear explanation and visual examples make complex physics concepts accessible.

Takeaways

• 📏 The video demonstrates using scale drawings to determine the resultant force on an object.
• 🚴‍♂️ An example is given of a cyclist applying a force of 4 newtons northward while a 3 newton force from the wind is blowing eastward.
• 📏 The forces are represented on a grid with arrows indicating direction and magnitude, where each newton is equivalent to one centimeter.
• 🔍 To find the resultant force, the two vectors are placed tip to tail and the magnitude is measured on the scale diagram.
• 📐 The direction of the resultant force is determined using a protractor to measure the angle from north.
• 🧭 The resultant force is calculated as 5 newtons at a bearing of 37 degrees from north.
• ⚖️ The concept of equilibrium is introduced, where forces balance out resulting in zero resultant force.
• 🔄 The order of arranging vectors does not affect the resultant force when they form a closed shape, indicating no resultant force.
• 🔄 The video also covers resolving vectors, which is the process of breaking down a vector into its horizontal and vertical components.
• 🛣️ An example of resolving a 50 newton force on a toy car going up a ramp is provided, using a scale of 10 newtons per centimeter.
• 📏 The resolved components are measured and converted to find the horizontal and vertical forces, resulting in 40 newtons to the right and 30 newtons upwards.

Q & A

What is the purpose of using scale drawings in the video?

The purpose is to find the resultant force on an object by representing forces as vector arrows on a grid and using a scale to convert measurements.

What scenario is used to explain the concept of resultant force?

The scenario of a man on a bike peddling northwards with a force of 4 newtons while a strong breeze blows him eastwards with a force of 3 newtons is used.

How are the forces represented on the grid in the example?

The forces are represented as a four-centimeter arrow upwards for the northward force and a three-centimeter arrow to the right for the eastward force, with each centimeter representing one newton.

What method is used to find the magnitude and direction of the resultant force?

The two vector arrows are placed tip to tail, and the resultant force is found by drawing a line from the starting point to the end point. The length of this line is measured and converted using the scale.

How is the resultant force measured and converted using the scale?

The resultant force is measured to be five centimeters, which is then converted to five newtons using the scale where one centimeter equals one newton.

How is the direction of the resultant force determined?

The direction is determined by measuring the angle between the resultant force and the north vector using a protractor, which gives an angle of around 37 degrees.

What does it mean if the forces all balance?

If the forces all balance, the object is at equilibrium, meaning there is no resultant force acting on it.

How can forces be shown to balance on a grid?

Forces can be shown to balance by arranging the vector arrows tip to tail. If they form a perfect triangle, it indicates zero resultant force.

What is the process of resolving vectors?

Resolving vectors involves splitting a force into its horizontal and vertical components using a scale drawing.

How is a vector resolved into its components in the toy car example?

The 50 newton force is represented by a 5 centimeter line at the same angle as the ramp. Horizontal and vertical lines are drawn from the ends of this line, measured, and converted using the scale to find the horizontal and vertical components.

Outlines

00:00

🚴‍♂️ Finding Resultant Force with Scale Drawings

This paragraph introduces the concept of using scale drawings to determine the resultant force on an object. It illustrates a scenario with a man on a bike applying a force of 4 newtons northward while a 3 newton force from a breeze is pushing him eastward. The forces are represented on a grid, with each newton equating to a centimeter. The resultant force is found by placing the vectors tip to tail and measuring the magnitude with a ruler, which in this case is 5 centimeters or 5 newtons. The direction is determined using a protractor, yielding an angle of 37 degrees from north. The paragraph also explains the concept of equilibrium when forces balance out, resulting in zero resultant force, and the importance of arranging vectors tip to tail regardless of order.

🔍 Resolving Vectors with Scale Drawings

The second paragraph delves into the process of resolving vectors, which is the opposite of finding the resultant force. It uses the example of a toy car being pushed up a ramp with a 50 newton force. The force is represented on a 10 newtons per centimeter scale, and the force's direction is aligned with the ramp's angle. The force is then resolved into its horizontal and vertical components by drawing perpendicular lines to the ramp's surface and measuring the lengths of these lines. The horizontal component is found to be 40 newtons to the right, and the vertical component is 30 newtons upwards. This process is essential for understanding how a single force can be broken down into its directional components.

Keywords

💡Scale Drawings

Scale drawings are graphical representations where objects are depicted in proportion to their actual size, using a consistent scale. In the video, scale drawings are used to visually represent and calculate forces acting on objects, such as the cyclist and the toy car, providing a clear and simplified method to understand complex vector calculations.

💡Resultant Force

The resultant force is the single force that represents the vector sum of all the forces acting on an object. It is crucial in determining the net effect of multiple forces. In the script, the resultant force on the cyclist is found by combining the forces due to pedaling and the wind, resulting in a force of 5 newtons at a 37-degree angle.

💡Neutrons

While 'neutrons' typically refers to subatomic particles in physics, in the context of this video, it seems to be a typographical error for 'newtons,' which is the unit of force in the International System of Units (SI). The script uses '4 neutrons' to describe the force exerted by the man pedaling his bike northwards.

💡Vector

A vector is a quantity that has both magnitude and direction. In the video, forces are represented as vectors, with arrows indicating direction and length representing the magnitude. The concept is central to understanding how forces combine and resolve into resultant forces or components.

💡Equilibrium

Equilibrium in physics means a state where all forces acting on an object cancel each other out, resulting in no net force and no change in the object's motion. The script illustrates equilibrium with an example of a particle with three forces acting on it, which when arranged tip to tail, show no resultant force.

💡Protractor

A protractor is a tool used to measure angles. In the context of the video, a protractor is used to measure the angle of the resultant force, which helps in determining the direction of the force acting on the cyclist.

💡Ramp

A ramp is a sloping surface that allows movement from a lower to a higher level or vice versa. In the script, a toy car is pushed up a ramp, and the force exerted on the car is resolved into horizontal and vertical components, which is essential for understanding the motion on an inclined plane.

💡Horizontal and Vertical Components

In physics, resolving a vector into its horizontal and vertical components involves breaking down a force into two perpendicular components. The script demonstrates this by resolving the force exerted on a toy car into a horizontal component (to the right) and a vertical component (upwards) when pushed up a ramp.

💡Toy Car

The toy car in the script serves as an example to illustrate the concept of resolving forces. It helps viewers understand how a single force can be decomposed into components that act in different directions, specifically along the horizontal and vertical axes.

💡Like and Subscribe

While not a scientific term, 'like and subscribe' is a common call to action in video content, encouraging viewers to engage with the video by liking it and subscribing to the channel for more content. It is part of the script's conclusion, aiming to increase viewer interaction and channel growth.

Highlights

The video demonstrates using scale drawings to determine the resultant force on an object.

A man on a bike creates a force of 4 newtons northward while a breeze exerts 3 newtons eastward.

Forces are represented on a grid with the cyclist as an orange dot and arrows indicating forces.

Each newton is equivalent to one centimeter in the scale diagram.

The resultant force is found by placing vector arrows tip to tail and drawing a line from start to end.

The magnitude of the resultant force is measured with a ruler and converted using the scale.

The direction of the resultant force is measured with a protractor.

An example shows a resultant force of 5 newtons at a bearing of 37 degrees from north.

Equilibrium occurs when forces balance, resulting in zero resultant force.

Three forces acting on a particle can be arranged tip to tail to find the overall force.

The order of arranging forces does not affect the resultant force calculation.

Vectors can be resolved into their horizontal and vertical components using a scale drawing.

A toy car example illustrates resolving a 50 newton force on a ramp.

The 50 newton force is represented by a 5 centimeter line at the ramp's angle.

Horizontal and vertical components are found by drawing perpendicular lines and measuring them.

The resolved force components are 40 newtons to the right and 30 newtons upwards.

The video concludes with an encouragement for likes and subscriptions for more content.

Transcripts

in this video we're going to look at how

we can use scale drawings

to find the resultant force on an object

let's imagine that a man on his bike is

peddling to create a force of 4 neutrons

northwards

at the same time though a strong breeze

is blowing him eastwards with a force of

3 newtons

we can represent this situation on a

grid

where the cyclist is this orange dot

and the forces are shown as a four

centimeter arrow upwards

and a three centimeter arrow to the

right

so that each newton is equal to one

centimeter

now that we have a scale diagram

we can find the magnitude and direction

of the resultant force by placing these

two vector arrows tip to tail

which we could do by moving this one up

here

so that the tip of the north vector

is just touching the tail of the east

vector

then to find the resultant force we just

draw a line from the starting point over

to the end point

and because our drawing is the scale

we can just measure it with a ruler to

see how long it is

in this case five centimeters

and then we can convert that into

neutrons using our scale

so because each centimeter is one newton

our resultant force would be five

newtons

to find the direction of the force

we just measure this angle here with a

protractor

which would give us around 37 degrees

so we could say that the resultant force

is 5 newtons at a bearing of 37 degrees

from north

in some cases the forces might all

balance

in which case the object will be at

equilibrium

for example if we had a particle that

had these three forces acting on it

then to find the overall force we just

arrange the three arrows tip to tail

like before

and because they all join up perfectly

like this

it means there must be zero resultant

force

don't worry about arranging the arrows

in any particular order though

as long as you put them all tip to tail

then you'll be fine

for example we could have arranged them

like this instead

they still form a perfect triangle which

means there's no resultant force

the last thing we need to look at is how

to resolve vectors

this is basically the opposite of what

we've been doing so far in this video

when you resolve a vector the aim is to

split it up into its horizontal and

vertical components

and to do this in practice we need to

use a scale drawing again

let's imagine that we have a toy car

and that we're exerting a force of 50

newtons on it to push it up the ramp

how do we resolve this force

well if we make our scale 10 newtons per

centimeter

then we could represent the 50 newton

force with a 5 centimeter line at the

same angle as the ramp

then all we have to do is draw a

horizontal line down here

and a vertical line up here

putting an arrow on each of them so that

we know their directions

then we just measure them with a ruler

to find that they're four centimeters

and three

centimeters and so looking at our scale

we can convert them to find that they

must be a 40 newton force to the right

and a 30 newton force upwards

so we've now resolved the 50 newton

force into its horizontal and vertical

components

that's everything for this video though

so i hope you enjoyed it if you did then

please do give us a like and subscribe

and hopefully we'll see you again soon