Download Centre of Gravity, Stability, Friction File

Mechanics L3
–
Mass and weight
Centre of Gravity
Stability
Friction
IFP 30th October 2014
Objectives:
• Differentiate
between mass and
weight
• Define Centre of
Mass.
• Explain stability
• Practice a
moments question
• Define 3 types of
friction
Key Words
Centre of Mass, centre
of gravity, stability,
moments, Friction,
coefficient of friction
Weight and mass –reminder
• How can I lose lots of weight quickly?
(Effective but very expensive)!
• Go to the moon!
• Mass is the amount of matter
(“stuff”) in an object measured in kg.
Invariant for a given object.
• Weight is the force caused by gravity
acting on that mass. newtons.
• W = mg.
• g on earth taken as 9.8 N Kg-1
Objectives:
• Differentiate
between mass and
weight
• Define Centre of
Mass.
• Explain stability
• Practice a
moments question
• Define 3 types of
friction
Key Words
Centre of Mass, centre
of gravity, stability,
moments, Friction,
coefficient of friction
More on g
• g is 9.81 N/kg at the surface of
Earth
• Due to earth’s shape value of g
varies slightly
• changes from 9.78 N/kg (at
equator) to 9.81 N/kg (at the poles)
• Note it’s g not G: this matters!
Objectives:
• Differentiate
between mass and
weight
• Define Centre of
Mass.
• Explain stability
• Practice a
moments question
• Define 3 types of
friction
Key Words
Centre of Mass, centre
of gravity, stability,
moments, Friction,
coefficient of friction
Centre of Gravity
• Centre of gravity of a body: the
point where its weight is
considered to act
• Sometimes called centre of mass
(the same thing effectively)
Objectives:
• Differentiate
between mass and
weight
• Define Centre of
Mass.
• Explain stability
• Practice a
moments question
• Define 3 types of
friction
Key Words
Centre of Mass, centre
of gravity, stability,
moments, Friction,
coefficient of friction
Stability
• An object resting on a surface is in equilibrium under the
influence of gravity if the CM is vertically above its base.
• If CM is not completely above its base then a turning
force (torque) is produced - it will topple over
• For stability, need wider base, low CM
When will the bus topple?
Objectives:
• Differentiate
between mass and
weight
• Define Centre of
Mass.
• Explain stability
• Practice a
moments question
• Define 3 types of
friction
Key Words
Centre of Mass, centre
of gravity, stability,
moments, Friction,
coefficient of friction
Moments – practice question
A uniform 10.0 kg beam 3.0 m long is hinged to a wall
and supported by a horizontal rope to make a 40º angle with the
wall.
A 15 kg mass hangs from the end of the beam.
What is the tension in the rope?
•
•
•
•
Torque about the wall is produced by:
Weight of beam
Tension of rope
Hanging weight
Objectives:
• Differentiate
between mass and
weight
• Define Centre of
Mass.
• Explain stability
• Practice a
moments question
• Define 3 types of
friction
Key Words
Centre of Mass, centre
of gravity, stability,
moments, Friction,
coefficient of friction
Solving this…
Take moments about point x.
Find all the moments trying to turn the
beam clockwise:
Mass: 15 *9.8 * 3 sin 40⁰
beam: 10 * 9.8 * 1.5 sin 40⁰
X
Find all the moments trying to turn the beam anticlockwise:
Tension in rope: T * 2 cos 40 ⁰
Total clockwise = total anticlockwise (Principle of moments)
Do the math(s)
T = 247N
Friction
• Occurs when two unattached
surfaces in contact (try to) slide or
roll relative to each other
• Due to roughness of both surfaces
• Proportional to normal force
• Always act in direction opposite to
slippage direction
• Reminder – Normal force acts at 90⁰ and
stops object falling through support
Objectives:
• Differentiate
between mass and
weight
• Define Centre of
Mass.
• Explain stability
• Practice a
moments question
• Define 3 types of
friction
Key Words
Centre of Mass, centre
of gravity, stability,
moments, Friction,
coefficient of friction
Three kinds of friction
• Static friction (s)
surfaces NOT sliding yet, but trying to
• Kinetic friction (k)
Objectives:
• Differentiate
between mass and
weight
• Define Centre of
Mass.
• Explain stability
• Practice a
moments question
• Define 3 types of
friction
surfaces sliding
• Rolling friction (r )
one surface rolling over the other
Key Words
Centre of Mass, centre
of gravity, stability,
moments, Friction,
coefficient of friction
More on friction
• Friction = μ x Normal force (Ff = μ Fn)
• μ: coefficient of friction, is a measure
of the strength of friction
– Scalar quantity, no units
Objectives:
• Differentiate
between mass and
weight
• Define Centre of
Mass.
• Explain stability
• Practice a
moments question
• Define 3 types of
friction
– Depends on both surfaces
– Does not depend on size of contact
area
• - Ratio of the frictional force to the
normal reaction between the surfaces
Key Words
Centre of Mass, centre
of gravity, stability,
moments, Friction,
coefficient of friction
Simple friction problem
• Mass of block = 10kg
• Coefficient of friction μ = 0.50
• How much force must be applied horizontally to
move the block at a steady speed?
Simple friction problem
• Mass of block = 10kg
• Coefficient of friction μ = 0.50
Fr
Applied dragging force
Ff
Weight
• Weight = 10 *9.8 = 98N (down)
• Reaction force = 98N (up)
• Ff = μ * Fr = 0.5 * 98 = 49N
Friction Problem
• A box that weighs 10.0 N is being dragged with constant
velocity along a horizontal surface of the table by a rope
that is at an angle α of 45° with that surface.
• The tension in the rope is 5.0 N.
• What is the coefficient of friction?
• Start by drawing a diagram representing the problem
Resolve applied pulling force F :
F1 = F cosα
(1)
F2 = F sinα
(2)
The normal force is Fg – F2
So the frictional force is:
Ff = (Fg – F2) μ
(3)
μ is the coefficient of kinetic friction
F1 must be equal to the Ff.
Therefore – some maths:
F cosα = (Fg – F2) μ
Substituting F2 from Eq. 2 :
F cosα = (Fg – F sinα) μ
and solving for μ:
μ = F cosα / (Fg - F sinα)
Put the numbers in: μ = 0.55
(4)
(5)
(6)