mechanics l3 – mass and weight centre of gravity stability friction ifp 30 th october 2014
DESCRIPTION
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 -1TRANSCRIPT
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Mechanics L3 –
Mass and weightCentre of Gravity
Stability Friction
IFP 30th October 2014
![Page 2: Mechanics L3 – Mass and weight Centre of Gravity Stability Friction IFP 30 th October 2014](https://reader036.vdocuments.us/reader036/viewer/2022083119/5a4d1acd7f8b9ab059970408/html5/thumbnails/2.jpg)
Objectives:• Differentiate
between mass and weight
• Define Centre of Mass.
• Explain stability• Practice a
moments question• Define 3 types of
friction
Key WordsCentre of Mass, centre of gravity, stability, moments, Friction, coefficient of friction
![Page 3: Mechanics L3 – Mass and weight Centre of Gravity Stability Friction IFP 30 th October 2014](https://reader036.vdocuments.us/reader036/viewer/2022083119/5a4d1acd7f8b9ab059970408/html5/thumbnails/3.jpg)
Objectives:• Differentiate
between mass and weight
• Define Centre of Mass.
• Explain stability• Practice a
moments question• Define 3 types of
friction
Key WordsCentre 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
![Page 4: Mechanics L3 – Mass and weight Centre of Gravity Stability Friction IFP 30 th October 2014](https://reader036.vdocuments.us/reader036/viewer/2022083119/5a4d1acd7f8b9ab059970408/html5/thumbnails/4.jpg)
Objectives:• Differentiate
between mass and weight
• Define Centre of Mass.
• Explain stability• Practice a
moments question• Define 3 types of
friction
Key WordsCentre 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!
![Page 5: Mechanics L3 – Mass and weight Centre of Gravity Stability Friction IFP 30 th October 2014](https://reader036.vdocuments.us/reader036/viewer/2022083119/5a4d1acd7f8b9ab059970408/html5/thumbnails/5.jpg)
Objectives:• Differentiate
between mass and weight
• Define Centre of Mass.
• Explain stability• Practice a
moments question• Define 3 types of
friction
Key WordsCentre 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)
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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
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Objectives:• Differentiate
between mass and weight
• Define Centre of Mass.
• Explain stability• Practice a
moments question• Define 3 types of
friction
Key WordsCentre of Mass, centre of gravity, stability, moments, Friction, coefficient of friction
When will the bus topple?
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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
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Objectives:• Differentiate
between mass and weight
• Define Centre of Mass.
• Explain stability• Practice a
moments question• Define 3 types of
friction
Key WordsCentre of Mass, centre of gravity, stability, moments, Friction, coefficient of friction
![Page 10: Mechanics L3 – Mass and weight Centre of Gravity Stability Friction IFP 30 th October 2014](https://reader036.vdocuments.us/reader036/viewer/2022083119/5a4d1acd7f8b9ab059970408/html5/thumbnails/10.jpg)
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
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
X
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Objectives:• Differentiate
between mass and weight
• Define Centre of Mass.
• Explain stability• Practice a
moments question• Define 3 types of
friction
Key WordsCentre of Mass, centre of gravity, stability, moments, Friction, coefficient of friction
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
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Objectives:• Differentiate
between mass and weight
• Define Centre of Mass.
• Explain stability• Practice a
moments question• Define 3 types of
friction
Key WordsCentre 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) surfaces sliding
• Rolling friction (r ) one surface rolling over the other
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Objectives:• Differentiate
between mass and weight
• Define Centre of Mass.
• Explain stability• Practice a
moments question• Define 3 types of
friction
Key WordsCentre 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– Depends on both surfaces– Does not depend on size of contact
area• - Ratio of the frictional force to the
normal reaction between the surfaces
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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?
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Simple friction problem• Mass of block = 10kg• Coefficient of friction μ = 0.50
• Weight = 10 *9.8 = 98N (down)• Reaction force = 98N (up)• Ff = μ * Fr = 0.5 * 98 = 49N
Ff
Fr
Weight
Applied dragging force
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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
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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 frictionF1 must be equal to the Ff.
Therefore – some maths:F cosα = (Fg – F2) μ (4)Substituting F2 from Eq. 2 :F cosα = (Fg – F sinα) μ (5)and solving for μ:μ = F cosα / (Fg - F sinα) (6)Put the numbers in: μ = 0.55