1.3 Mass and weight

LOs:
• Show familiarity with the idea of the mass of a body
• State that weight is a force
• Distinguish between mass and weight
• Recall and use the equation W = mg
• Recall and use the relation between force, mass and acceleration (including the direction), F = ma
• Demonstrate understanding that weights (and hence masses) may be compared using a balance
Supplement
• Demonstrate an understanding that mass is a property that ‘resists’ change in motion
• Describe, and use the concept of, weight as the effect of a gravitational field on a mass

Task
Define what mass and weight are. Describe the differences between them.

Mass from youtube Eureka episode
Mass & Weight from youtube Eureka episode


Mass
The mass of an object is how much matter it is composed of. It is measured in kilograms [kg].
Mass is independent of gravity. It is the same anywhere in the Universe.
Mass is also known as the resistance to move. - This is called INERTIA.

Weight

The force of gravity on an object is its weight. It is measured in Newtons [N].

Weight is a vector and a force. Its force depends upon 2 things.
  • gravitational acceleration
  • mass
Weight is caused by the gravitational field of Earth on a mass.
F = mg
  • m is mass
  • g is acceleration due to gravity

ie) Lorries are harder to jump start than cars.
Weight is a force -> We can compare weights using a balance. Hence we can compare masses.

The Mass vs Weight song by Mr. Edmonds YouTube


Force Gravity and Weight from BBC GCSE BITESIZE
Gravity and Weight from Newton's homepage
Planet from BBC BITESIZE

Newton's 1st law (Inertia)

Everything at rest will stay at rest unless there is a force applied to it.
Everything in motion will stay in motion unless there is a force applied to it.

Newton's 2nd law

Force = mass x acceleration

The bigger the force acting on the object, the bigger the acceleration it gives to the object.
Quantity
Symbol
SI unit
force
F
The unit of weight (force) is the Newton, N
mass
m
The unit of mass is the kilogram, kg
acceleration
a
The unit of acceleration is the metres per second squared, m/s2
Figure 3.10 on your text page 31. The increasing speed of a falling ball image shows the acceleration due to the gravity acting on it.


Question A
A car of mass 1000Kg moving at 15 m/s hits a barrier and stops in a time of 0.1 s.

(a). Calculate its deceleration.

(b). What force would the car experience?


Question B
A hovercraft moves on a cushion of air which is trapped underneath it. The trapped air reduces friction.

(a) The hovercraft starts from rest and as it starts the propeller produces a forward force F of 22,000 N. The mass of the hovercraft is 25,000 kg.
Calculate the initial acceleration of the hovercraft. You may assume there is no friction.

(b) Some time later, the hovercraft reaches a steady speed, even though the force F is unchanged. Suggest, in terms of the forces acting on the hovercraft, why the speed is now constant?


Click the link and solve the Quizz on Force, Gravity, Mass, Weight.

Newton's 3rd law

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


1.5 Forces


1.5.5 Scalars and vectors
Supplement
• Understand that vectors have a magnitude and direction
• Demonstrate an understanding of the difference between scalars and vectors and give common examples
• Add vectors by graphical representation to determine a resultant
• Determine graphically the resultant of two vectors

Scalar and vector quantities

  • Scalars: Magnitude (or numerical value) ONLY Ex) speed, mass, energy, density, distance, temperature; 3m, 900calories, 7oC
  • Vectors:Magnitude and a direction Ex) velocity, force, weight, acceleration; 3m North, 7m/s East
    • Some Properties of Vectors;
    1. can be manipulated algebraically,
    2. can be combined graphically or by calculation




Addition of parallel vectors.

The resultant vector must have magnitude and direction.

2 Vectors in the same direction; The resultant force is the addition of two vectors acting in the same direction.

2 Vectors in the opposite direction; The resultant force is the addition of two vectors acting in towards the bigger force's direction.


Addition of non-parallel vectors using the parallelogram method

The resultant force is represented by the diagonal of the parallelogram. It also gives us the direction of the resultant force.


Addition of non-parallel vectors using the tip-to-tail method

The resultant force is found by joining the start point of a force to the end point of another force. A triangle is thus formed and the resultant force can be measured.

1.5.1 Effects of forces
LOs
• Recognise that a force may produce a change in size and shape of a body
• Plot extension/load graphs and describe the associated experimental procedure
• Describe the ways in which a force may change the motion of a body
• Find the resultant of two or more forces acting along the same line
• Recognise that if there is no resultant force on a body it either remains at rest or continues at constant speed in a straight line
• Understand friction as the force between two surfaces which impedes motion and results in heating
• Recognise air resistance as a form of friction

Force:




A force is a push or pull in a particular direction.
A force causes acceleration since it changes in the speed or direction of an object.
A force is measured in Newtons[[N].
Forces usually cannot be seen but their effects can.
Forces usually acts in pairs. Forces can push or pull in any direction and more than one force can act on an object at a time.
Ex) A force of 10N is roughly the amount of force the Earth's gravity pulls on a 1 kg mass.

EXERCISE: Fill in the blanks below
1. A force can cause a stationary object to start moving.
2. A force can cause a moving object to increase speed.
3. A force can cause a moving object to decrease speed.
4. A force can cause a moving object to change its direction of motion.
5. A force can represented by arrows.

Resultant force:

The resultant force is the single force that has the same effect as two or more forces acting on it.
The combination of all the forces acting on an object is the net/resultant force.

The net force is equal to the sum of the two forces when two forces act in the same direction on an object.
The net force is equal to the difference of the two forces when two forces act in opposite directions on an object.

Balanced forces;

If two forces of equal strength act on an object in opposite direction, resulting in a net force of zero and no change of motion, forces are balanced.
Two or more opposite forces acting on an object and if their effects cancel each other and they do not cause a change in an object's motion is known as balanced forces.

If the effects of the forces don't cancel each other, if one force is stronger than others, the forces are unbalanced.
Unbalanced forces cause a change in motion; speed or direction or both


For an object with zero acceleration, the different forces acting on it are balanced or add up to zero; the resultant(or net force) is zero.
Fig 3.6 b on your text page 29.

Falling through the air

Describe a speed against time graph for a falling parachutist. Explain what the terminal velocity is.
Skydiving
Task: Plot a speed against time graph of a falling parachutist in the animation.
( Graph of terminal velocity during a parachute jump from absorblearning.com)

Terminal velocity

As a skydiver jumps out of a plane she accelerates because gravity pulls her down. The air resistance increases as her speed increases and so she starts to slow down. She reaches a terminal velocity - but at this speed she would most probably splat when she hits the ground. By using a parachute, she increases her air resistance and so lower her terminal velocity so that it is safer to land.

Notice that a parachutist's weight is constant. When air resistance equals weight, the forces are balanced and the parachutist reaches a steady speed. This is called as the terminal velocity. The acceleration is upwards when she opens her parachute, then she reaches at the new terminal velocity.

Fig 3.13 and 3.14 on your text page 33.

Supplement
• Describe qualitatively motion in a circular path due to a perpendicular force (F = mv 2/r is not required)

Circular motion

Any object moving along a circular path is changing direction as it goes. An object following a circular path is acted on by a force at right angles to its velocity.
Fig A and B on your text page 48.

Supplement
  • Interpret extension/load graphs
  • State Hooke’s Law and recall and use the 
expression F = kx
  • Recognise the significance of the term ‘limit of proportionality’ for an extension/ load graph
  • Recall and use the relation between force, mass and acceleration (including the direction)
  • Describe qualitatively motion in a curved path due to a perpendicular force
(F = mv2/r is not required)
Homework
Plot a graph showing extension vs load using a spring. Add the line of the best fit and determine/explain the relationship between independent and dependent variables. Do workbook page 19 - 21.

Supplement
• State Hooke’s Law and recall and use the expression F = k x, where k is the spring constant
• Recognise the significance of the ‘limit of proportionality’ for an extension-load graph

Hooke's Law

The extension of a spring is directly proportional to the force applied to it, provided the elastic limit is not exceeded.

F = -kx

F is the restoring force of a spring.
x is displacement from equilibrium
k is spring constant [ unit: N/m ]
Point 1: Hooke's law holds only within certain limitations.
Point 2: Negative indicates the direction of the force

Example 1:
A mass m stretches a spring a distance x. How far will 5m stretch it?
5 times
Example 2:
A 300g mass stretches a spring 50cm. What is the spring constant?
F = -kx, (300g x 10m/s2 ) = -k (50cm), (0.3kg x 10m/s2) = -k (0.5m), k= -6 N /m
Example 3:
How far will a force of 6 x 103N stretch a spring with spring constant 3 x 104 N /m?


Hooke’s law ( The extension of a spring is directly proportional to the force applied to it ) is valid only up to the proportionality limit of a material. Beyond this limit, Hooke’s law no longer applies. Beyond the elastic limit, the material remains deformed even when the stress is removed.

Elastic limit:
•The material no longer shows elastic behaviour (ie The spring does not return to original size when stretching force is removed)
•The material is permanently deformed ie The spring is larger or longer than originally
•The material is weaker as the above effects are caused by fracture of some atomic bonds


Hooke's law Elastic Limit.jpg
Image from physconcepts

Deformation of materials is also critical in vehicle design though in practice the terms stress( the force per square metre ) and strain ( the extension per unit length ) are more commonly used instead of simply force and extension; stress is directly proportional to strain



Hooke's law from Britannica
Hooke's law from BBC GCSE Bitesize





Forces and elasticity questions from BBC GCSE Bitesize

FORCE
1) Explain Newtons first law of motion
2) What is the unit of measure for force?
3) How is mass ‘converted in to weight’
4) A 25Kg sack of potatoes is lifted in to a 2M high shelf. What is the weight of the sack and how much work is done on it?
5) Write down the formula for momentum
6) A cart is travelling at 20m/s. Its mass is 500Kg. What is the cars momentum?
7) A car has a momentum of 200Kgm/s. It turns left…explain how it’s momentum changes
8) Suggest 5 things that could affect braking distance
9) Suggest 5 things that could affect thinking distance
10) A driver has a reaction time of 0.5 seconds. What is the thinking distance if she is driving at 30m/s?
11) A car of 500Kg at 10m/s travelling east to west, crashes in to a car travelling west to east. The second car has a mass of 750N and is travelling at 5m/s. On impact the first car comes to a halt. What happens to the second car?
12) Write down and explain Newtons second law of motion
13) A force of 600N is used to push an asteroid of mass 200Kg. What is the acceleration of the asteroid?
14) An car engine produces a force of 1500N. Friction opposes motion with a force of 750N. The vehicle mass is 600Kg. What is the acceleration
15) Write down Newtons third law of motion
16) Explain in terms of the forces, why a parachutist reaches a terminal velocity before and after she opens her parachute
TRY AS MANY AS YOU CAN. 10 MINIMUM


Forces revision from BBC GCSE Bitesize


1.5.2 Turning effect
• Describe the moment of a force as a measure of its turning effect and give everyday examples
• Understand that increasing force or distance from the pivot increases the moment of a force
• Calculate moment using the product force × perpendicular distance from the pivot
• Apply the principle of moments to the balancing of a beam about a pivot
Supplement
• Perform and describe an experiment (involving vertical forces) to show that there is no net moment on a body in equilibrium
• Apply the idea of opposing moments to simple systems in equilibrium

1.5.3 Conditions for equilibrium
• Recognise that, when there is no resultant force and no resultant turning effect, a system is in equilibrium
Supplement
• Perform and describe an experiment (involving vertical forces) to show that there is no net moment on a body in equilibrium

Turning effect of forces

Balancing a beam.
Experiment: Turning Effect of Forces
Watch the video clip The lever

Moment: The measure of its turning effect of a force about a pivot.

1. The moment of a force is bigger if the force is bigger.
2. The moment of a force is bigger if it acts further from the pivot.
3. The moment of a force is the greatest if it acts at 90o to the object it acts on.

Moment = force x perpendicular distance from pivot to force = F x d
  • where F= force [in N]
  • d = perpendicular distance from pivot [in m]
The SI unit of the moment of a force is the newton metre [N m].
The moment (Turning effect) describes with magnitude in N m and direction as clockwise or anticlockwise.

When a system is in equilibrium, the resultant force is zero and the resultant turning effect is zero.
  • Total clockwise moment = Total anticlockwise moment.

Equilibrium: the state of being balanced due to the zero resultant force.

Law of the lever.mp4

Question A
A student conducts the following experiment on a half-metre rule to feel the turning effect of a force
(a) If the weight W is placed at the 15cm mark to the left from 0 cm mark, find the moment of the force applied by a hand when holding the ruler horizontally at the position between 40 cm and 50 cm to the far left.
(b) He then shifts the same weight W to the 5 cm mark and finds that it is more difficult now to maintain the half-metre rule in a horizontal position than before in (a). Why is this so?

Homework

Pivots and Levers and Calculating Moments from Intel Education

Do questions on your Revision p.28



1.5.4 Centre of mass
• Perform and describe an experiment to determine the position of the centre of mass of a plane lamina
• Describe qualitatively the effect of the position of the centre of mass on the stability of simple object


When drawing two vertical lines from the pin points across the lamina toward the centre of gravity, the point where lines cross is the centre of mass. The position of the centre of mass affects the stability of an object.
The lower the centre of mass is, the more stable it becomes.

WEIGHT - The force of gravity on a body. W = mg, where W is weight/ N; m is mass/ kg; g is gravitational field strength/ Nkg-1. On Earth, g = 9.81 Nkg-1
weight_astronaut.gif


FRICTION: The force which opposes motion when one surface moves over another. It is caused by the roughness of the surfaces.
NORMAL REACTION: Two objects in contact each exert a force on the other which is perpendicular to the surface.
TENSION: A force produced in a body when opposing forces are stretching it. The opposite is a compression force when two forces are squashing a body.
UPTHRUST: An upward force on a body which is immersed in a fluid (liquid or gas).
LIFT: An upward force on the wing of an aircraft due to the air flowing around it.

INERTIA: The property of matter which makes it resist acceleration.

Newton’s first law of motion.
Newtons-First-Law.jpg
NEWTON’S FIRST LAW OF MOTION: A body continues to maintain its state of rest or of uniform motion in a straight line unless acted upon by an external unbalanced force.

Condition for translational equilibrium.
TRANSLATIONAL EQUILIBRIUM: When the net force on an object is zero in all directions (ie no linear acceleration).

Newton’s second law of motion.
F = ma can be expressed as F = Δp/Δt
F_pt_from_DB.png

NEWTON’S SECOND LAW OF MOTION: ∑F = ma The rate of change of momentum of an object is proportional to the applied force and takes place in the direction in which the force acts.

Newton_fma.gif

Problems involving Newton’s second law.

Newton_law_2calculation.jpg

NEWTON’S THIRD LAW OF MOTION: Whenever a particle A exerts a force on another particle B, B simultaneously exerts a force on A with the same magnitude in the opposite direction.
When two bodies A and B interact, the force that A exerts on B is equal and opposite to the force that B exerts on A.

PCLM_boat.gifPCLM_explosion

IMPULSE: The change in momentum. A vector. Unit is Ns
LINEAR MOMENTUM: the product of mass and velocity. It is a vector measured in kgms-1
pmv_from_DB.png
Impulse_from_DB.png

Impulse due to a time-varying force by interpreting a force–time graph.
F-t_graph2.gif
The law of conservation of linear momentum.
LAW OF CONSERVATION OF LINEAR MOMENTUM: The momentum of an isolated system remains constant (ie when no external forces are acting). Or, in any isolated system, the change in momentum is zero.

PCLM_calculationPCLM_collision.gif


Thank you for your hard work!
I will be collecting your physics folder on 22nd October Monday. Please submit it to me just before taking the test on Forces. Ms. Lee