1. basic physics

1. BASIC PHYSICS

Objective

(a) The 6 essential base SI units (kg, m, s, A, mol, K)

(b) Representing units in terms of the 6 base SI units and their

prefixes

(c) Checking equations for homogeneity using units

(d) the difference between scalar and vector quantities and to give

examples of each – displacement, velocity, acceleration, force,

speed, time, density, pressure etc

(e) the addition and subtraction of coplanar vectors, and perform

mathematical calculations limited to two perpendicular vectors

(f) how to resolve a vector into two perpendicular components

(g) the concept of density and how to use the equation to

calculate mass,

density and volume

(h) What is meant by the turning effect of a force

(i) The use of the principle of moments

(j) The use of centre of gravity, for example in problems including

stability: identify its position in a cylinder, sphere and cuboid

(beam) of uniform density

(k) when a body is in equilibrium the resultant force is zero and

the net moment is zero, and be able to perform simple

calculations

SPECIFIED PRACTICAL WORK

Practical

Measurement of the density of solids

Determination of unknown masses by using the principle of moments

Finding Units

1. Which of the following equations are correct? Check for homogeneity

(a) g

LT

2

1 Where T is time, L a length and g acceleration

(b) rmvF 2 where F is force, m is mass, v is velocity and r is

distance.

(c) 2mvE Where E is energy, m is mass and v is velocity

(d) d

pc where c is velocity, p is pressure and d is density

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2. The drag coefficient CD of a car moving with speed v through air of

density ρ is given by:

Av

FCD 2

21

where F is the drag force and A is the maximum cross sectional area of

the car. Show that CD is unitless.

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Vector Addition

1. A cable car in operation has a weight of 2.5 x 104N. It is blown by high

wind which produces a sideways force of 5000N. Assuming that the car

is not moving, find the tension in the cable and the angle it hangs at.

Draw a vector diagram and check your answer by calculation.

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2. A skydiver falling vertically experiences a net vertical force of 500N. A

sideways gust of wind exerts a force of 100N. What are the magnitude

and direction of the resultant force on the sky-diver?

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3. Two ropes are tied to a large boulder. One rope is pulled with a force of

400N due east. The other rope is pulled with a force of 300N due south.

What is the magnitude and direction of the resultant force on the

boulder?

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Resolving Forces

1. Water flows from a nozzle with an initial velocity of 5.8ms-1 at an angle of

45º to the horizontal. Show that the horizontal component of the velocity is

4.1ms-1.

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2. A mirror weighs 30N. It hangs from a wire which passes over a nail in the

wall. The wire on each of the nail makes an angle of 30 with the horizontal.

What is the tension in the wire?

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Moments

1. For each of the following, say whether it is balanced or not.

If the object is not balanced, say which way it will turn (Clockwise or anticlockwise).

(a) (b) 2. For each of the following, say whether it is balanced or not.

If the object is not balanced, say which way it will turn (Clockwise or anticlockwise).

(a)

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5N 6N

6cm 5cm

10N 3N

4cm

15cm

20N

12N

5N

30cm 10cm

30cm

(b)

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3. Each of these objects does balance. Fill in the missing numbers. (a) …………………………………………………………………………………………

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12N

6N

9cm 7cm

15cm

20N

3N 2N

9cm a

4. This uniform metre rule is balanced. 0 10 20 30 40 50 60 70 80 90 100

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2N 1N e

Classwork 1.

Uncertainties

Homework 1

1.

2. KINEMATICS Objective

(a) What is meant by displacement, mean and instantaneous

values of speed, velocity and acceleration

(b) The representation of displacement, speed, velocity and

acceleration by graphical methods

(c) The properties of displacement-time graphs, velocity-time

graphs, and interpret speed and displacement-time graphs for

non-uniform acceleration

(d) How to derive and use equations which represent uniformly

accelerated motion in a straight line

(e) How to describe the motion of bodies falling in a gravitational

field with and without air resistance - terminal velocity

(f) The independence of vertical and horizontal motion of a body

moving freely under gravity

(g) The explanation of the motion due to a uniform velocity in

one direction and uniform acceleration in a perpendicular

direction, and perform simple calculations


Practical

Measurement of g by freefall

Distance, Speed and Acceleration

Questions

A graph to show how distance changes with time

for a runner

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12

Time in Seconds

Dis

tan

ce i

n m

etr

es

1. Label on the graph an area of constant speed

2. Label on the graph an area where the person is at rest.

3. What is the speed between 0-2s?

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Using Displacement-time graphs

A graph to show how displacement changes with

time

-30

-20

-10

0

10

20

0 5 10 15 20

Time in seconds

Dis

pla

cem

en

t in

Metr

es

1. What is the velocity between 0 and 2 seconds?

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A graph to show how speed changes with time

0

10

20

30

40

50

60

0 5 10 15 20

Time in seconds

Sp

eed

in

m/s

1. What is the acceleration between 2 and 5 seconds?

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2. What is the acceleration between 16 and 18 seconds?

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3. What is the total distance travelled between 0 and 6 seconds?

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4. Between 0 and 6s, where is the largest acceleration? How can you tell?

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The Equations of Motion

Example 1

A particle moves in a straight line with uniform acceleration 5ms-2. It starts from rest

when t=0. Find its velocity when t=3s.

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Example 2

A particle moves in a straight line. When t=0 its velocity is 3ms-1. When t=4s its

velocity is 12ms-1. Find its acceleration.

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Example 3

A car moves in a straight line with constant retardation (deceleration) 4ms-2. When

t=3s its velocity is 5ms-1. Find its initial velocity.

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Example 4

A particle moves in a straight line with constant acceleration 5ms-2. How long will it

take for the car’s velocity to increase from 2ms-1 to 24ms-1?

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Example 5

A particle starts from rest and moves in a straight line with constant acceleration

4ms-2 for 3s. How far does it travel?

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Example 6

A ball is thrown vertically upwards with a velocity of 20ms-1. Calculate:

(a) the maximum height reached,

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(b) the total time that the ball is in the air.

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Now try these questions

1. A particle is moving in a straight line with a constant acceleration of 6.0ms-2. As it

passes a point, A, its speed is 20ms-1. What is its speed 10s after passing A? [4]

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2. A particle which is moving in a straight line with a velocity of 15ms-1 accelerates

uniformly for 3.0s, increasing its velocity to 45ms-1. What distance does it travel whilst

accelerating? [4]

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3. A car starts to accelerate at a constant rate of 0.80ms-2. It covers 400m whilst

accelerating in the next 20s. What was the speed of the car when it started to

accelerate? [4]

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4. A car moving at 30ms-1 is brought to rest with a constant retardation of 3.6ms-2.

How far does it travel whilst coming to rest? [4]

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Projectile Motion

Example 1

A stone is thrown over the edge of a cliff with a horizontal velocity of 15ms-1.

The cliff is 150m high.

Ignoring any air resistance, and taking g = 9.81ms-2, calculate:

(a) the time it takes for the stone to reach the ground.

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(b) The distance it lands from the foot of the cliff.

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(c) the magnitude of the stone’s velocity when it hits the ground.

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Example 2

A golfer hits a ball so that it moves off with a velocity of 26ms-1 at 30º to the

horizontal. Ignoring any air resistance and taking g =9.81ms-2, Calculate:

(a) the time that the ball is in the air.

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(b) the horizontal distance the ball travels.

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Questions

1. A golf ball is hit at 26ms-1 at 45º to the ground. Ignoring air resistance:

(a) How long is the ball in the air for?

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(b) How far does the ball travel horizontally?

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(c) What is the maximum height the ball reaches during its flight?

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2. A particle is projected with a velocity of 30ms-1 at an angle of 40º above the

horizontal plane.

Find:

(a) the time for which the particle is in the air.

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(b) the horizontal distance it travels.

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Homework 1.

3. DYNAMICS Objective Resource

(a) the concept of force and Newton's 3rd law of motion

(b) how free body diagrams can be used to represent forces on a

particle or body

(c) the use of the relationship Resultant Force F = ma in

situations where mass is constant

(d) the idea that linear momentum is the product of mass and

velocity

(e) the concept that force is the rate of change of momentum,

applying this in situations where mass is constant

(f) the principle of conservation of momentum and use it to solve

problems in one dimension involving elastic collisions (where

there is no loss of kinetic energy) and inelastic collisions (where

there is a loss of kinetic energy)


Practical

Investigation of Newton’s 2nd law

Newton’s 2nd Law of Motion

Example 1

A computer base unit of mass 4.5 kg is dragged along a smooth desk. If the

tension in each arm of the person dragging it is 16 N and acts at 22◦ above

the horizontal, then what is the normal reaction force?

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Now try these:

1. A computer base unit of mass 7.5 kg is dragged along a smooth desk. If the

normal contact force is 23 N and the tension in the arm of the person dragging

it acts at 23◦ to the horizontal, then what is the total tension in the person’s

arms?

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2. Two tug boats are towing a large boat, of mass 22500 kg, back to shore.

Tug boat 1 is pulling with a force of 5500 N at an angle of 35◦ north of the

forward motion and tug boat 2 is pulling with a force of 4907.8 N at an angle

40◦ south of the forward motion. If the large boat is being pulled with constant

velocity, and there is a resistive force to the motion, then what size is the

resistive force?

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3. Two tug boats are towing a large boat, of mass M kg, back to shore. Tug

boat 1 is pulling with a force of T1 N at an angle of 25◦ north of the forward

motion and tug boat 2 is pulling with a force of T2 N at an angle of 25◦ south of

the forward motion. If the large boat is being pulled with constant velocity, and

there is a resistive force of 4000 N to the motion, then what are the

magnitudes of the two forces T1 and T2?

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4. A child on a sledge is being pulled along a horizontal path by its parent.

The child and sledge have a combined mass of 20 kg and there is a normal

contact force of 124.5 N. Given there is no resistance to motion and the

parent pulls with a force of 125 N at an angle θ to the horizontal, then what is

the angle θ?

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Classwork 1.

Forces on an Inclined Plane

Example 1

A 2 Kg box is put on the surface of an inclined plane at 27 ° with the horizontal.

The surface of the inclined plane is assumed to be frictionless.

a) Draw a free body diagram of the box on the inclined plane and label all

forces acting on the box.

b) Determine the acceleration a of the box down the plane.

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c) Determine the magnitude of the force exerted by the inclined plane on the

box.

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Example 2

A particle of mass 5 Kg rests on a 30° inclined plane with the horizontal. A

force Fa of magnitude 30 N acts on the particle in the direction parallel and up

the inclined plane.

a) Draw a Free Body Diagram including the particle, the inclined plane and all

forces acting on the particle with their labels.

b) Find the force of friction acting on the particle.

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c) Find the normal force exerted by the inclined on the particle.

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Momentum Examples

Example 1:

The cars are stuck together after the collision and car B is at

rest

What is the velocity of cars after the collision?

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Before After

3kg 5kg

At rest u=2ms-1

5kg 3kg

v

Example 2:

The cars are stuck together after the collision and car B is

moving before the collision


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Before After

2kg 3kg

u2=1ms-1 u1=2ms-1

3kg 2kg

v

Example 3:

The cars are stuck together after the collision and cars A and

B

are moving in the opposite direction


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Example 4:

The cars are not stuck together after the collision and car A is at

rest before the collision

What is the velocity of car 2 after the collision?

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Before After

2kg 3kg

u2=1ms-1 u1=2ms-1

3kg 2kg

v

v2

Before After

5kg 10kg

At rest u1=5ms-1

10kg 5kg

v1= 2ms-1

Example 5:

The cars are not stuck together after the collision and both cars are moving#

before the collision


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v2=3ms-1

Before After

4kg 2kg

u2=2ms-1 u1=5ms-1

2kg 4kg

v1

Example 6:

The cars are not stuck together after the collision and cars A

and B are moving in opposite directions before the collision


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v2=3ms-1

Before After

4kg 2kg

u2=2ms-1 u1=5ms-1

2kg 4kg

v1

Example 7

What is the velocity of car 2 before the collision?

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v2=6ms-1

Before After

10kg 2kg

u2 u1=5ms-1

2kg 10kg

v1=3ms-1

Using Newton’s Second Law

Example 1

If the collision occurs in 0.5s, what is the force exerted on truck A by B?

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Work out the force exerted on B by A.

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Before After

3kg 5kg

At rest u=2ms-1

5kg 3kg

V = 0.75ms-1

Using the velocities you have calculated, find the forces on

trucks A.

1. Time = 0.25s

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2. Time = 0.2s

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Before After

2kg 3kg

u2=1ms-1 u1=2ms-1

3kg 2kg

v

Before After

2kg 3kg

u2=1ms-1 u1=2ms-1

3kg 2kg

v

3.Time = 0.02s

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Elastic and Inelastic Collisions

Find out if these are elastic or inelastic

Example 1

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v2

Before After

5kg 10kg

At rest u1=5ms-1

10kg 5kg

v1= 2ms-1

v2=3ms-1

Before After

4kg 2kg

u2=2ms-1 u1=5ms-1

2kg 4kg

v1

1.

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2.

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v2=3ms-1

Before After

4kg 2kg

u2=2ms-1 u1=5ms-1

2kg 4kg

v1

v2=6ms-1

Before After

10kg 2kg

u2 u1=5ms-1

2kg 10kg

v1=3ms-1

Classwork

Homework 1

1.

Homework 2 1.

1. basic physics

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