Forces and motion - Shawon Notes

Physics > Section 1: Forces And Motion

a) Units

1.1 use the following units: kilogram (kg), metre (m), metre/second (m/s), metre/second2 (m/s2), newton (N), second (s), newton per kilogram (N/kg), kilogram metre/second (kg m/s).

Unit of mass=Kilogram (kg)
Unit of distance=Metre (m)
Unit of speed or velocity= Metre per second (m/s)
Unit of acceleration= metre per second2 (m/s2)
Unit of Force= Newton(N)
Unit of Time= Second(s)
Unit of gravitional acceleration= Newton per kilogram(N/kg)
Unit of Momentum= kilogram metre per second (kg m/s)

b) Movement and Position

1.2 plot and interpret distance-time graphs

Distance: The change of position of an object is called distance. The diagram shows an example:

Diplacement: The change of position of an object in a particular direction is called displacement.

This shows another object changes its position from C to D through curved path but the displacement will be straight distance from C to D.

A distance-time graph represents the speed or velocity of any object. In this graph the object is moving at 1 m per second. It is in a constant speed. In a distance-time graph, distance should go to the Y-axis while time should go over the X-axis.

Speed= gradient=distance/time = 3m/3s= 1m/s

Few points that should be noted

  1. In a displacement – time graph or distance- time graph, the average velocity is found by the ratio (△s)/(△t) where △s = change in displacement/distance and △t=time interval
  2. A positive gradient of the displacement-time graph indicates that the car is moving in the same direction as the displacement.
  3. A negative gradient of the displacement-time graph indicates that the car is moving in the opposite direction to the displacement.
  4. A zero gradient of the displacement-time curve shows that the car is stationery.
Some explanation of motion from graph:

Zero displacement

Constant displacement

Not moving

Acceleration

Deceleration

1.3 know and use the relationship between average speed, distance moved and time:

Speed: Speed is defined as the rate of change of distance. In other words, speed is the distance moved per unit time. It tells us how fast or slow an object is moving.

Average speed: Average speed is the total distance moved divided by total time taken.

Instantaneous speed:  The speed of an object at a particular moment is called instantaneous speed. It is measured by taking ratio of distance travelled by shortest possible time.

The difference between speed and velocity:

Speed Velocity
i. The rate of distance travelled is speed. i. The rate of displacement travelled is velocity.
ii. Speed can be in any direction. ii. Velocity is speed in particular direction.
iii. Speed is a scalar quantity. iii. Velocity is a vector quantity.

1.4 describe experiments to investigate the motion of everyday objects such as toy cars or tennis balls

Experiment: Measuring speed using light gate

  1. Attach a cart of measured length centrally to the top of the toy car.
  2. Air track ensures a frictionless way for the toy car.
  3. A gentle push can move the toy car at a steady speed.
  4. Arrange for the card to block a light gates beam as it passes through it.
  5. Electronic timer measures how long the card takes to pass through the beam.
  6. Now calculate the toy car's average velocity as it passes the light gate by: v = length of the card / interruption time

1.5 know and use the relationship between acceleration, velocity and time:

Acceleration is the rate at which objects change their velocity. The rate of decease of velocity is called deceleration. It is just a negative acceleration. It is defined as follows:

acceleration = (final velocity - initial velocity)/ time taken

1.6 plot and interpret velocity-time graphs

Velocity-time graphs represent the acceleration of any object. Velocity(m/s) is in the Y-axis while Time is the X-axis.

Some common velocity-time graphs:

1.7 determine acceleration from the gradient of a velocity-time graph

Acceleration = gradient
= (y2 - y1)/(x2 - x1 )
= (200-0)/(50-0)
= 4 ms2

1.8 determine the distance travelled from the area between a velocity-time graph and the time axis.

Distance can be determined by finding the area under a velocity-time graph as shown below

Distance travelled = area under the graph
= 1/2(a+b)h
= 1/2(100 + 40) x 150
= 1/2 x 140 x 150
= 10500 m

c) Forces, movement, shape and momentum

1.9 describe the effects of forces between bodies such as changes in speed, shape or direction

Force is that which can change the state of rest or uniform motion of an object. Force is simply pushes and pulls of one thing on another.

If a body is thrown up in the air, what is the effect of gravity on the body? At first gravity reduces the speed of upward movement of the body and at a certain height it stops. So Force effects the speed.
Take a sponge and squeeze it will change its shape.
Throw a ball at a person in one direction. That person will hit the ball again i.e. apply force to the ball and it will change its direction.

To sum up the examples, the effects that occur when a force is applied to an object are:

  • The object may start to move or stop moving.
  • The object may speed up or slow down.
  • The object may change its shape
  • The object may change its direction of movement.

1.10 identify different types of force such as gravitational or electrostatic

Different sorts of Force:

  • Gravitional force or weight: The pull of earth due to gravity.
  • Normal Reaction: Simple reaction that stops something when to apply force to it.
    E.g.: A book is kept on the table which has a normal reaction on it. Otherwise the book would fall down.
  • Air Resistance: The resistivity or drag in the air while an object moves is called Air Resistance.
    E.g.: When a parachutist open the parachute the movement slows down for the opposite force acting in it.
  • Upthrust: Upthrust force acts only on liquid or air. It pushes an object upwards inspite of gravity.
    E.g.: A helium balloon moves upwards due to up thrust force.
  • Magnetic: Magnetic force is the attraction force between the poles of magnets. N=S
  • Electrostatic: Electrostatic force is the attraction force between charges. +=-
  • Tension: The pull at both ends of a stretched spring ,string, or rope
  • Frictional force: the force produced when two objects slide one over another is called frictional force.

1.11 distinguish between vector and scalar quantities

Scalar quantities are physical quantities that have magnitude only.

Vector quantities however are physical quantities that possess both magnitude as well as direction.

Scalar Vector
Mass Displacement
Time Velocity
Distance Acceleration
Speed Force
Volume
Density
Work
Energy
Power

1.12 understand that force is a vector quantity

Force is a vector quantity due to the following reasons -
  • It has magnitude i.e has the value of its size.
  • It has direction.
  • When applied force, an object moves with particular motion in a fixed direction.
E.g: Gravitional force has one direction which is downwards. Upthrust has the direction of upwards.

1.13 find the resultant force of forces that act along a line

Forces which act along a straight line can be added if the forces are in the same direction or subtracted if the forces are in the opposite direction. The force that you get after adding or subtracting is called the resultant force. The resultant force is a single force that has the same effect as all the other forces combined.

Figure a shows that two forces: 150N and 50N are acting on an object A in the same direction and the object is moving.

Figure b shows that a single from 200N is acting on the same object and the object moves at the same motion. So 200N is the resultant force of 150N and 50N.

1.14 understand that friction is a force that opposes motion

Friction is the force that causes moving objects to slow down and finally stop. The kinetic energy of the moving object is converted to heat as work is done by the friction force. Friction occurs when solid objects rub against other solid object and also when objects move through fluids (liquids and gases).

Friction reduces efficiency of machines and cause wastage. It also wears and tears the surface.

It can be reduced by making the surface smooth using lubricating oils.

However, friction is the reason we can walk, or write. It is helping us in various ways.

1.15 know and use the relationship between unbalanced force, mass and acceleration:

Balanced and Unbalanced force: When a force acting on an object is equal to the force opposing the object the forces are “balanced.”In this case the object will not move. If a force acting on an object is “NOT” equal to the force opposing, then the object the forces are “unbalanced.” In this case the object will move to the direction at which force is acting higher.

Force= mass x acceleration
In equation, F=ma (where, m=mass and a=acceleration)
F α a

Force is directly proportional to acceleration. If force increases acceleration increases.

1.16 know and use the relationship between weight, mass and g:

Weight is the pull of earth. To calculate it, use the formula: Weight = mass x gravitional acceleration
W =mg
In earth g= 10 m/s2 if there is no opposite force.

1.17 describe the forces acting on falling objects and explain why falling objects reach a terminal velocity

In a free falling object two types of force acts: Drag and Weight. The size of the drag force acting on an object depends on its shape and its speed. If the drag force of an object increase to a point which is equal to Weight, then the acceleration stops. It falls in a constant velocity known as terminal velocity.

Reaching terminal velocity on a parachute:

When a skydiver jumps from a plane at high altitude he will accelerate for a time and eventually reach terminal velocity. When he will open her parachute this will cause a sudden increase in the drag force. At that time drag force will be higher than the weight and he will decelerate for sometime. Later those forces will become equal and reach a new terminal velocity.

1.18 describe experiments to investigate the forces acting on falling objects, such as sycamore seeds or parachutes

Experiment: Measuring the force of a falling ball using light gate

Apparatus required: Cylinder, light gate, data logger, electric balance

First, we measure the weight of the ball using an electric balance. This is the force acting downwards all the time.

Set up the cylinder using light gate at different points keeping the same distance difference between each of them. Fill the cylinder with oil or any other liquid. For more accurate results, we will be using a cylinder with a diameter close to the diameter of the ball.

Now release the ball from the top of the cylinder. After it reaches the bottom, we will notice that the time taken between each light gates increases as it go downwards. We can calculate the acceleration from that. Since, F = ma, we can calculate the resultant force.

That means, the resistance acting on the increases. At a time, the resistance will equal the weight, and the forces will be balanced. It will then fall with a constant velocity.

1.19 describe the factors affecting vehicle stopping distance including speed, mass, road condition and reaction time

The stopping distance is the sum of Thinking distance and Braking distance.

Thinking Distance: The distance travelled after seeing an obstacle and till reaction.

Braking Distance: The distance travelled after the brakes are applied.

The thinking distance depends on the following factors -

  • Whether the driver is tired or has taken alcohol or drugs.
  • On the visibility power of the driver.
  • On the speed of the car.
  • The braking distance depends on the following factors -

  • Speed of the car: The more the speed is, the more the braking distance will be; S α V2.
  • Mass of the car: As acceleration is equal to F/m, for constant braking force, the more is the mass, the less is the deceleration, the more is the braking distance.
  • Road condition: If the road is rough, the braking distance will be less.
  • Tyre condition: If the tyre is new (rough), there will be less braking distance.
  • Braking system: For loose braking system, the braking distance will be more.
  • 1.20 know and use the relationship between momentum, mass and velocity:

    Momentum is a quantity possessed by masses in motion. Momentum is measure of how difficult it is to stop something that is moving. We calculate the momentum of a moving object using the formula: Momentum,p(kg m/s) = mass, m(in kg) x velocity, v (in m/s)
    P = m x v

    1.21 use the idea of momentum to explain safety features

    Objects in a car have mass, speed and direction. If the object, such as a person, is not secured in the car they will continue moving in the same direction (forward) with the same speed (the speed the car was going) when the car abruptly stops until a force acts on them.

    Every object has momentum. Momentum is the product of a passenger's mass and velocity (speed with a direction). In order to stop the passenger's momentum they have to be acted on by a force. In some situations the passenger hits into the dashboard or windshield which acts as a force stopping them but injuring them at the same time.

    Cars are now designed with various safety features that increase the time over which the car’s momentum changes in an accident. Crumple zones are one of the safety features now used in modern cars to protect the passengers in an accident. The car has a rigid passenger cell with crumple zones in front and behind. During a collusion, it creases the time during which the car is decelerating. This also reduce the force impacting on the passenger increasing their chances of survival.

    Many cars are now fitted with air bags to reduce the forces acting on passengers during collisions again by extending the time of deceleration. Air bags are detected by devices called accelerometers that detect the rapid deceleration that occurs during a collision. The purpose of an airbag is to help the passenger in the car reduce their speed in collision without getting injured. An airbag provides a force over time. This is known as impulse. The more time the force has to act on the passenger to slow them down, the less damage caused to the passenger.

    1.22 use the conservation of momentum to calculate the mass, velocity or momentum of objects

    Force x time = increase in momentum

    If a moving object hits another slow or stationary object, it will result an equal force to both of the objects (according to Newton’s Third Law). That forces act in opposite directions and obviously for the same amount of time. This means the F x t for each is the same size. The moving object lost its momentum while the stationary object gained its momentum. So it is balanced. The total moment of the two objects is unchanged before and after the collision - momentum is conserved.

    Momentum before the collision = momentum after the collision
    (f x t) + (f x t) = (f x t) (f x t)

    1.23 use the relationship between force, change in momentum and time taken:

    Initial momentum of object= mu
    Final momentum= mv
    Therefore increase in momentum = mv-mu
    Rate of increase of momentum= (mv-mu)/t

    (mv – mu)/t
    m(v-u)/t
    ma=Force
    Force = Rate of increase of momentum
    Force = Change in momentum / time

    1.24 demonstrate an understanding of Newton’s third law

    Newton’s thirds law: “For every action there is an equal and opposite reaction.”
    Newton’s third law states four characteristics of forces:

    • Forces always occur in pairs (action and reaction force.)
    • The action and reaction are equal in magnitude.
    • Action and reaction act opposite to one another.
    • Action and reaction act on different bodies.

    1.25 know and use the relationship between the moment of a force and its distance from the pivot:

    moment = force × perpendicular distance from the pivot
    moment =F x d

    The turning effect of a force about a hinge or pivot is called its moment. It is measured in Newton meter (Nm).

    1.26 recall that the weight of a body acts through its centre of gravity

    The centre of gravity of an object is the point where the whole weight appears to act. So if we support the centre of gravity of the object, the object wont fall no matter how wide it is. Because the moment of the all sides are balanced and there will be no clockwise or anti-clockwise movement.

    1.27 know and use the principle of moments for a simple system of parallel forces acting in one plane

    Here, the pivot is placed in the centre of the beam which balances it upon the pivot. All the weight is acting upon it. If the pivot is moved leftwards, the distance on the right hand side will be higher and we will see a clockwise turning effect.

    1.28 understand that the upward forces on a light beam, supported at its ends, vary with the position of a heavy object placed on the beam

    An object weighing 400 N is placed in the middle of the beam. The beam is not moving,so the upward and downward forces must be balanced. As the object is placed in the middle of the beam, the upward forces on the ends of the beam are same as each other. If it is moved right to one end of the beam, then the upward force will all be at that end of the beam. As it is moved along the beam, the upward forces at the ends of the beam change. In c) he is ¼ away from the plant. The upward force on the support nearest to him is ¾ of his weight and the upward force on the end of furthest beam is only ¼ of his weight.

    1.29 describe experiments to investigate how extension varies with applied force for helical springs, metal wires and rubber bands

    Experiment: Investigating extension with applied force in spring

    Apparatus: Spring/Wire/Rubber-band, Scale, Some masses, Clamp and stand, mass hanger

    Working procedure:

    1. Take the length of the normal condition.
    2. Add a mass in the mass hanger and determine the extension by using the porter and the scale.
    3. Add another mass gradually and determine the extension in all cases.
    4. Plot a graph of extension and relevant loads.
    5. Observation with helical spring:

      Since the graph of load & extension is a straight line, which proves the extension and load are directly proportional.

      Observation with rubber band:

      Since the graph didn’t produce a straight line, extension is not directly proportional to load force. But extension still increases as the force is applied.

      Observation with metal wire:

      1.30 understand that the initial linear region of a force-extension graph is associated with Hooke’s law

      Hooke’s law, “Within the elastic limit, extension is directly proportional to the load i.e. e α f”

      Hooke measured the increase in length (extension) produced by different load forces on springs. The graph he obtained by plotting force against extension looked like that below. This straight line passing through the origin shows that the extension of the spring is proportional to the force. The relationship is known as Hooke’s law.

      Hooke’s Law only applies if you do not stretch a spring to far. At a point the elastic limit it starts to stretch more for each successive increase in the load force. Once you have stretch a spring beyond this limit it has changed shape permanently and will not return to its original shape.

      1.31 describe elastic behaviour as the ability of a material to recover its original shape after the forces causing deformation have been removed.

      Objects showing elastic behaviour has the ability to return to its original shape after the forces causing its shape are removed. Examples of objects showing elastic behaviour are coiled springs.

    d) Astronomy

    1.32 understand gravitational field strength, g, and recall that it is different on other planets and the moon from that on the Earth

    The strength of gravity on a planet or moon is called its gravitational field strength. But this force depends upon

    • The masses of the two objects
    • The distance between the masses

    The greater the mass the greater the gravitional force. As the mass the mass in everyday objects are less, gravitional force is almost negligible. It is noticeable in planets, stars, sun etc.

    The greater the distance the lower the gravitional force. If you move 50000 km away from Earth, you won’t fall down as the force is between you and the earth is very weak.

    Gravitional Field Strength of Planets and Moon

    Objects GFS (N/kg)
    Mercury 4
    Venus 9
    Earth 10
    Moon 1.6
    Mars 4
    Jupiter 23
    Saturn 9
    Uranus 9
    Neptune 11

    1.33 explain that gravitational force:

    • causes moons to orbit planets
    • causes the planets to orbit the sun
    • causes artificial satellites to orbit the Earth
    • causes comets to orbit the sun

    Planets are held in orbit by the gravitional pull of the Sun. Similarly comets orbit the sun and moons and satellites orbit the planet. It is the gravitional attraction between this mass and each of the planets that holds the Solar System together and causes the planets to follow their curved paths.

    1.34 describe the differences in the orbits of comets, moons and planets

    Comets: Comets orbit the Sun. Their orbits are very elongated. At times they are very close to the Sun , while at other times they are found at the outer reaches of the Solar System. As a comet gets close to the Sun, the gravitational forces acting upon it increase and it speeds up. At the opposite end of its orbit, a long way from the Sun, the gravitation forces are smaller, so the comet travels at its slowest speed.

    Moons: Moons orbit a planet. The Earth has just one moon.The Moon, like the Earth spins on its axis, but much more slowly than the Earth turns. It completes one full rotation every 29.5 days. Because the time it takes to complete one orbit around the Earth is the same as the time for one rotation. The Moon always keeps the same part of its surface facing the Earth.

    Planets: Planets orbit the Sun. The closest planet follows a much more tightly curved path than the furthest one. They all move in ellipses.

    1.35 use the relationship between orbital speed, orbital radius and time period:

    The speeds of satellites vary greatly depending on the tasks they are performing. The speed of satellite can be calculated using the equation:
    orbital speed=(2 x π x orbital radius)/(time period)
    v= 2πr/T

    1.36 understand that:

    • the universe is a large collection of billions of galaxies
    • a galaxy is a large collection of billions of stars
    • our solar system is in the Milky Way galaxy.

    The Universe is mainly empty space within which are scattered large numbers of galaxies- astronomers believe that there are billions of galaxies in the Universe. The distances between galaxies are millions of times greater than the distances between stars within a galaxy.

    Gravitional forces between stars cause them to cluster together in enormous groups called galaxies. Galaxies consist of billions of stars. Our galaxy is called spiral galaxy or the Milky Way and our nearest star is the Sun.

    Bengali Biology Chemistry English Language
    ICT Physics Mathematics B F. Pure Maths
    Revision Notes