Mechanics L3 – Mass and weight Centre of Gravity Stability Friction IFP 30 th 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

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)

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

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 When will the bus topple?

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 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

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 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) surfaces sliding Rolling friction (r ) one surface rolling over the other

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 friction Friction = μ x Normal force (F f = μ F n ) 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

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 Weight = 10 *9.8 = 98N (down) Reaction force = 98N (up) F f = μ * Fr = 0.5 * 98 = 49N FfFf FrFr Weight Applied dragging force

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 : F 1 = F cosα (1) F 2 = F sinα (2) The normal force is F g – F 2 So the frictional force is: F f = (F g – F 2 ) μ (3) μ is the coefficient of kinetic friction F 1 must be equal to the F f. Therefore – some maths: F cosα = (F g – F 2 ) μ (4) Substituting F 2 from Eq. 2 : F cosα = (F g – F sinα) μ (5) and solving for μ: μ = F cosα / (F g - F sinα) (6) Put the numbers in: μ = 0.55