Notesale: Turn your study into money

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Mechanics
26 January 2015

18:52

Work, energy and power
• Work = force x distance
○ W = Fd
• Forms of energy
○ Kinetic energy (Ek)
 Due to motion
○ Potential energy (Ep)
 Due to height/ position
• Mass
○ Form of energy
○ Energy contained


Linear motion
• Acceleration is the rate of change of velocity

Vectors and scalars
• Measurement of velocity and acceleration
○ Ticker tape timer
 Trolley moves along track
 Tape pulled through time r
 0
...
02
• Find acceleration
○
• Distance time graphs
○ Content speed
 Speed = slope

Distance

Mechanics Page 1

Distance

Time

• Velocity-time graphs
○ Accelerating body
○ Slope = acceleration
○ Area under graph
 Distance travelled

Velocity

Time

• Scalar
○ Only have magnitude
○ Mass (kg)
○ Length (m)
○ Time (s)
• Vector
○ Magnitude and direction
○ Velocity
○ Acceleration
○ Displacement

Vector addition
• Adding vectors
○ Two or more vectors replaced by one
• Known
○ How large single vector
○ What direction
• Forces
○ Two forces
□ 5N
□ 10N
 Push in same direction
 Replaced
□ 15N

10N
15N
5N

Mechanics Page 2

• Two forces
○ 5N and 10N
 Opposite directions
 Replaced
□ 5N forces

5N
10N

5N

• Angles
○ Triangle law
 Right angled triangle
 Pythagoras's Theorem

3N

4N

5N

Resultant
• Reprints single vector
• Calculated
5
○ Pytharous
3

4

Vector resolution
Mechanics Page 3

Vector resolution
• Every vectors
○ Resolved
 2 perpendicular vectors
• Example
○ Push object
 10N
 Angle
□ 45o

45o

10N

Object

• Same effect
○ Push across
 7
...
07N
• Calculate
○ Trigonometry
 10N
□ Hypotenuse
 Other two lengths
□ Across and down forces

45o

10

• Same applies for velocity
○ 40m/s at 30o to horizontal
 Horizontal velocity
□ 34
...
The rider can be pushed along so that it passes through each of the light gates
...
As it passes through one the light is blocked by the card
...

3
...
This procedure can be repeated to measure the velocity at the second gate, v
...
The acceleration can be calculated using the formula:
Conclusion
The velocity and acceleration have been measured
...
Set up the apparatus as shown in the diagram
...
Set the weights (F)
...

3
...

4
...
Remove 1N disc from the pan, attach this to the vehicle, and repeat
...
Continue for a number of values of F
...

7
...

Conclusion
A straight line through the origin shows, that for a constant mass, the acceleration is proportional to the applied
force
...

• The air track reduces friction, improving accuracy
...
Set up the apparatus as in the diagram
...
With the second vehicle (m2) stationary, give the first (m1) a gentle push
...
With the second vehicle (m2) stationary, give the first (m1) a gentle push
...

3
...
From these find the initial velocity u and the final velocity v
...
Calculate the momentum before the collision using the equation:
; and the momentum
after the collision using the equation:
5
...
Record the results
...


Accuray
• The air track reduces the effect of friction
• It is important to measure the velocities immediately before and after the collision, to offset the slowing
down due to friction
...
Set up the apparatus
...

2
...

3
...

4
...
Take the smallest time as the correct value for t
...
Repeat for different values of h
...

Obtain an average value for g
...


g=2(slope)
h/m

Mechanics Page 10

T2/s2

Accuracy
The shortest time is taken as the value for t because various factors can delay the falling of the ball, but nothing
should speed it up
...
Using the pump increase the pressure on the air in the tube
...
Record the volume v and the corresponding pressure P
...
Repeat for several values of P and v
...
Record the results
...
Plot a graph of P against 1/v
...
e
...


P/Pa

1/v/cm-3
Mechanics Page 11

1/v/cm-3

Accuracy
• It is important to allow the temperature to return to normal after the pressure has been changed
...


Investigation of the laws of equilibrium for a set of co-planar forces
Apparatus

Newton meter (forces acting up)

Metre stick

Weights (forces acting
down)

Method
1
...

2
...

3
...

Conclusion
1
...
They should be equal confirming
the first law of equilibrium
...
Calculate the total clockwise and anti-clockwise moments about the 0cm mark, the 50cm mark and one
other mark on the stick
...

Accuracy
• It is crucial that the metre stick should be horizontal when the readings are taken, so that the distances
are perpendicular to the forces
...


Investigation of the relationship between the period and length for a simple pendulum and
hence the calculation of g
...
Place the thread of a pendulum between two halves of a spilt cork
...
Set the pendulum swinging through a small angle (<10 o)
...
Divide this time t by thirty to get the periodic time T
...
Record both l and T
...
Repeat for different lengths, l, of the pendulum
...

The straight line through the origin will confirm that l is proportional to T 2
...

• Longer lengths will reduce the percentage error
...

• Ensure the point at where the strings meet is stationary
• Note the readings on the first two Newton meters
...

Observation
• According to Newton's third law this should be equal in magnitude but opposite in direction to Fr
...

• We can therefore use vector addition of this experimental method to find the resultant of two vectors
...
Set up the apparatus as shown in the diagram
...
Heat the can for a period with the lid removed so that the water boils
...
Remove the can from the heat and tightly replace the lid
...
Let the can cool
...

Conclusion
This demonstrates the effect of atmospheric pressure, which is acting on the outside of the can, but is no
longer balanced by an equal pressure from within
...
Set up the apparatus as shown
...
Hang the mass from the spring balance and note the reading
...
Hang the mass from the spring balance and note the reading
...
Lower the mass into the water and again note the reading
...
Find the weight of the displaced water
...
This is
the upward force experienced by the mass
...


Mechanics Page 16

Definitions
26 January 2015

18:53

Energy
Energy is the ability to do work

Work
Work is done when a force moves an object through a distance

Power
• The rate at which work is done
• The rate at which energy is converted from one form to another

Newton's Laws of Motion
1
...

2
...
(F=ma)
3
...


Friction
Friction is a force that tends to oppose motion

Principle of conservation of momentum
The principle of conservation of momentum states that in any interaction between bodies,
the total momentum before the interaction will equal the total momentum after the
reaction, provided no external forces act upon the bodies
...
Its direction is
towards the centre of the circle
...
Its direction is towards the centre
of the circle
...


Mechanics Page 17

Simple harmonic motion
Any motion where the acceleration (a) of a particle is proportional to its distance (s) from an
equilibrium position is simple harmonic motion
...


Density
The density of an object is its mass per unit volume

Pressure
Pressure is defined as force per unit area
...
(Pa)

Boyle's Law
This law states that, at a constant temperature, the pressure on a fixed mass of gas is
inversely proportional to its volume
...


Law of flotation
The law of flotation states that when body floats it is displacing exactly its own weight of
fluid
...
The sum of the forces in any direction equals the sum of the force in the opposite
direction
...
The sum of the moments about any point is zero
...
e
...

The angular velocity ω is given by:
The direction of the linear motion is at a tangent to the circle and is constantly changing
...
The force acting on the body is given by Newton's law of
gravitation to be:

And by

, to be:

Equating these two we can see that:

Satellites

Satellite; mass = m
r
M

Mechanics Page 20

Satellite; mass = m
r
M
Planet

Period (T) of a satellite
For satellites in orbit about a planet of mass M the centripetal force is equal to the gravitational force: i
...


But in terms of period T of a motion:

i
...
Kelpler's third law of planetary motion

The speed (v) of the satellite:
By the same logic:
Gives:

Simple harmonic motion
Hooke's law states that the force on a spring is proportional to the extension of the spring
...
e
...


Mechanics Page 22

(Hooke's law)

Equations
01 April 2015

16:50

Work, energy and power
 Crane
□ Weight
 1000kg
□ Distance
 30m
□ Time
 100 seconds
 Find
□ Work done
□ Power of crane
□ Find efficiency if it uses 500,000 J
 Answer
□ Work done



□ Efficiency



□ Power of crane



Mechanics Page 23



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