# mechanics one revision notes

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- Created on: 13-05-13 20:23

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### Page 1

www.mathsbox,.org.uk

Mechanics 1 Revision notes

1. Kinematics in one and two dimensions

EQUATIONS FOR CONSTANT ACCELERATION ARE NOT GIVEN Learn Them!

1 2 1 2

v = u + at s = ut + at s = vt at

2 2

1 2 2 s : displacement…

Mechanics 1 Revision notes

1. Kinematics in one and two dimensions

EQUATIONS FOR CONSTANT ACCELERATION ARE NOT GIVEN Learn Them!

1 2 1 2

v = u + at s = ut + at s = vt at

2 2

1 2 2 s : displacement…

### Page 2

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FREE FALL UNDER GRAVITY

Acceleration due

Assumptions

to gravity

- the body is a point mass

- air resistance can be ignored

- the motion of a body is in a vertical line

9.8 ms-2

- the acceleration due to gravity is constant Unless given in the

question

EXAMPLE…

FREE FALL UNDER GRAVITY

Acceleration due

Assumptions

to gravity

- the body is a point mass

- air resistance can be ignored

- the motion of a body is in a vertical line

9.8 ms-2

- the acceleration due to gravity is constant Unless given in the

question

EXAMPLE…

### Page 3

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Vector equations for constant acceleration the 5 equations involving, displacement,

velocity etc can be used

· If asked to write an equation in terms of t for displacement/ velocity etc simplify

your equation as far as possible by collecting the i terms and j terms

e.g u…

Vector equations for constant acceleration the 5 equations involving, displacement,

velocity etc can be used

· If asked to write an equation in terms of t for displacement/ velocity etc simplify

your equation as far as possible by collecting the i terms and j terms

e.g u…

### Page 4

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For questions involving river

Method 2 Lami's theorem

crossings and current you may

need to use the cosine rule as

T1 T2 12g well as the sine rule to calculate

= =

sin 128 sin 117 sin 115 missing lengths and angles

T1 = 102 N Cosine Rule…

For questions involving river

Method 2 Lami's theorem

crossings and current you may

need to use the cosine rule as

T1 T2 12g well as the sine rule to calculate

= =

sin 128 sin 117 sin 115 missing lengths and angles

T1 = 102 N Cosine Rule…

### Page 5

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Tension / Thrust pulling or pushing force on the body

Friction

· Always acts in a direction opposite to that in which the object is moving or

tending to move

· Smooth contact friction is small enough to be ignored

· Maximum Friction (limiting friction) -…

Tension / Thrust pulling or pushing force on the body

Friction

· Always acts in a direction opposite to that in which the object is moving or

tending to move

· Smooth contact friction is small enough to be ignored

· Maximum Friction (limiting friction) -…

### Page 6

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2nd Law F = ma Net Force = mass x acceleration

· Always work out and state Net force clearly before equating to ma

· Check - if acceleration is positive net force should also be positive

Example : A taut cable 25m long is fixed at 35º…

2nd Law F = ma Net Force = mass x acceleration

· Always work out and state Net force clearly before equating to ma

· Check - if acceleration is positive net force should also be positive

Example : A taut cable 25m long is fixed at 35º…

### Page 7

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Finding the acceleration

Coefficient of friction = 0.2 2g T = 2a Friction = 0.2R

T F = 6a R = 6g so F = 11.76 N

2kg 2g T = 2a

T 11.76 = 6a a = 0.98 ms-2

Force on the pulley

Resultant…

Finding the acceleration

Coefficient of friction = 0.2 2g T = 2a Friction = 0.2R

T F = 6a R = 6g so F = 11.76 N

2kg 2g T = 2a

T 11.76 = 6a a = 0.98 ms-2

Force on the pulley

Resultant…

### Page 8

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Displacement (r) : r = ut+ ½at2

2

r = Ut cosqi + (Ut sinq ½9·8t )j

Horizontal dispalcement Height ( vertical dispalcement)

after t seconds after t seconds

To find the range

Height component = 0

Solve 2

Ut sinq ½9·8t = 0

To find t

Substitute into…

Displacement (r) : r = ut+ ½at2

2

r = Ut cosqi + (Ut sinq ½9·8t )j

Horizontal dispalcement Height ( vertical dispalcement)

after t seconds after t seconds

To find the range

Height component = 0

Solve 2

Ut sinq ½9·8t = 0

To find t

Substitute into…

### Page 9

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Modelling Assumptions

Common Terms and Meanings

Term Applies to What is disregarded

Inextensible Strings, rods Stretching

Thin Strings, rods Diameter, thickness

Light Strings, springs, rods Mass

Particle Object of negligible size Rotational motion, size

Rigid Rods Bending

Small Object of negligible size Rotational motion

Smooth Surfaces, pulleys Friction

Assumptions…

Modelling Assumptions

Common Terms and Meanings

Term Applies to What is disregarded

Inextensible Strings, rods Stretching

Thin Strings, rods Diameter, thickness

Light Strings, springs, rods Mass

Particle Object of negligible size Rotational motion, size

Rigid Rods Bending

Small Object of negligible size Rotational motion

Smooth Surfaces, pulleys Friction

Assumptions…

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