mechanics Flashcards
moment of the force
The turning effect of a force is call the moment of the force
The moment of a force is defined by the equation:
ππππππ‘ ππ π πππππ (Nm) = πππππ (N) Γ Perpendicular distance from the pivot to the line of action of the force (m)
π=πΉπ
The Principle of Moments
If an object is balanced: the total clockwise moment about a pivot equals the total anticlockwise moment about that pivot.
Centre of Mass
The weight of an object may be considered to act at a single point referred to as the objects Centre of mass
Use the principle of moments to calculate the unknown forces and distance shown in the diagrams below:
lever
A lever is a rigid beam with a fulcrum. The effort (input force) is applied on one end of the beam and a load (output force) is applied to the other end of the beam. The fulcrum is the point on which the beam pivots.
The point at which the lever will just begin to move will be the point where the moment created by effort is equal to the moment created by the load.
principal of the lever
The moment of the load and effort are equal which means that if the effort is further from the pivot than the load (its perpendicular distance is greater) the effort must be smallerthan the load.
A pair of gears exert forces on each other that are equal in magnitude but opposite in direction, which means that adjacent gears rotate in opposite directions. Because the magnitude of the force on pair of gears is the same, the turning effect on the gear is directly proportional to the radius of the gear (which is the distance between the force and the pivot). However the larger the gear the lower the rate of radiation.
(π ππππ’π ππ πΊπππ π΄)/(π ππππ’π ππ πΊπππ π΅)=(ππ’ππππ ππ ππππ‘β π΄)/(ππ’ππππ ππ ππππ‘β π΅)=(ππππππ‘ ππ πΊπππ π΄)/(ππππππ‘ ππ πΊπππ π΅)=(π ππ‘π ππ πππ‘ππ‘πππ π΅)/(π ππ‘π ππ πππ‘ππ‘πππ π΄)
gear example
When two gears share the same axel they must have the same moment. Because they have the same moment the larger gear must exert a larger force,
Momentum
π=ππ£
momentum (Kgm/s) = mass (Kg) x Velocity (m/s)
βConservation of momentumβ meansβ¦
The momentum in a closed system remains constant
A toy train of mass 1kg is travelling at 3m/s when it collides with a second train of equal mass travelling in the opposite direction at 1m/s. They stick together due to magnetic catches. How fast do they travel immediately after impact?
Momentum before collision = Momentum after collision
(1x3)+(1x-1)= (2xv)
2=2v
v=1 m/s
The trains then slow down. Why is momentum no longer being conserved?
External forces such as air resistance and friction act on the trolleys (the momentum is transferred to the air /ground which are not part of the system)
Force and rate of change of momentum
πΉ=πβπ£/βπ‘
Resultant Force (N) = (Mass(kg) x Change in velocity(m/s)) / Change in time (s)
Safety features
Helmets, crash mat, seat belts, etc. all protect humans in a similar way:
They increase the time taken for a person to come to a stop
The change in momentum is the same
So the rate of change of momentum is lower
Which means the resultant force is less
Which means the risk of injury is reduced
inertia
the tendency of an object to continue in its state of rest or motion
Formula for pressure
Pressure (Pa) = Force (N) / Area (MΒ²)
P=F/A
The unit of pressure is the pascal (Pa)
One Pa is equal to one N/MΒ²
Pressure in a column of Liquid
As you move deeper in a liquid the pressure increases due to a greater weight of liquid above you.
The increase in pressure caused due to a column of liquid can be calculated with the equation:
pressure (Pa) =density (Kg/MΒ³) Γgravitational field strength (N/Kg) Γheight of column (M)
p= Οgh
Upthrust
The weight of fluid displaced by an object is equal to the upthrust acting on the object.
If an object is fully immersed the volume of fluid, it displaces is equal to its own volume.
A fully immersed object will float if the upthrust is greater than its weight, which is only true if the weight of the fluid displaced is greater than the weight of the object itself. The only way this can be true is if the density of the fluid is greater than the density of the object.
If an object is denser than the surrounding fluid it will sink
If an object is less dense than the surrounding fluid it will float
Atmospheric Pressure
Air molecules collide with a surface create atmospheric pressure.
At increasing altitude, the distance between air molecules increases.
So, the frequency of collisions of air molecules on the surface must decrease.
Which means that air pressure decreases with altitude.
effect of radiation on the earths temperature
1) During the day, lots of radiation (like light) is transferred to the Earth from the Sun and absorbed. This causes an increase in local temperature.
2) At night, less radiation is being absorbed than is being emitted, causing a decrease in the local temperature.
3) Changes to the atmosphere can cause a change to the Earthβs overall temperature. If the atmosphere starts to absorb more radiation without emitting the same amount, the overall temperature will rise until absorption and emission are equal again.
