Chapter 4 Forces, Density & Pressure Flashcards
a couple has a pure turning effect. Why?
- because a single force will tend to make an object accelerate (unless another force balances it)
- where a couple is a pair of equal, opposite forces = will not make object accelerate.
- The turning effect, well force is determined by its torque
balanced or unbalanced
- check whether an object remains balanced or start to rotate - calulate an unknown force or distance if we know the object is balanced
centre of gravity
the point where the entire weight of an object appear to act
finding moment of force (method 1)
-draw perpendicular line from the pivot to the line of the force - find the distance from pivot. -find force -calculate moment of force (F1 x x2) -we see that: x2 = d sin(angle) hense: moment = F2 x d sin(angle) x2 = distance from pivot to 90 degree of F2 line(figure 4.17)
find the moment (method 2)
calculate the component of F2 that is at 90 to the lever.
-this is F2 sin(angle).multiply by d moment = F2 sin(angle) x d
For an object to be in equilibrium two conditions must be met?
-resultant force acting on the object is zero -the resultant moment is zero
how to resolve a force F into its horizontal and vertical components
horizontal component of F, Fx = F cos(angle) vertical component of F, Fy = F sin(angle)
moment of a force Def
of a force about a point is the product of a force and perpendicular distance from the line of action of the force to the point.
moment of force =
force x distance from pivot depends on two forces: -magnitude of force -perpendicular distance of the force from pivot Torque=FD Torque= Nm Force = F Distance= the perpendicular force from pivot (meters)
principle of moments
the sum of clockwise moments about a point is equal to the sum of the anticlockwise moments about the same point provided the body is in equilibrium
resolving
to split a vector (such as force) into two vectors at right angles
to form a couple, the two forces must be:
-equal in magnitude -parrel, but opposite in direction -separated by a distance
torque def
the product of one of the forces and the perpendicular distance between the forces. (the turning effect or moment of a couple)
torque of a couple =
one of the forces x separation of forces Torque about O = (F x OA) + (F x OB) O = FD
two forces at a right angle (drawn) (Combining vectors)
-first draw a horizontal arrow to represent the Force -Next, starting from the end of this arrow, draw the second arrow in the irection its effecting -now, draw a line from the start to the end of the second arrow ( represent resultant force ) -resulatant force = scaled diagram or by calculation (phytagorus theorm)
what is a couple
a pair of equal and opposite forces that act on an object at different points and produce rotation only Can not produce translation motion
what is a triangle of forces (Combining vectors)
a closed triangle drawn for an object in equilibrium. The sides of the triangle represent the forces in both magnitude and dircetion
what is equilibrium mean (Combining vectors)
an object in equilibrium is either at rest or traveling with constant velocity because the resultant force on it is zero
Electric force
The force acting on an electric charge due to the electric field F= EQ E- Energy field N per coloum Q- Charge
Gravitational force
The force acting on a ,ass due to the gravitational field F= MG
Types of forces
-gravitational force -electrical force -upthrust and buoyancy -frictional and viscous forces
Upthrust or buoyancy
The reactions force acting against the weight of a body in a liquid
Frictional and viscous forces
Friction - is the force that resists the motion of a body (mew) Viscous- resistive force to a liquid flow or gas (gamma)
Density
- Density is the mass per unit volume of an object
- Objects made from low-density materials typically have lower mass. For example, a balloon is less dense than a small bar of lead despite occupying a larger volume
- The units of density depend on what units are used for mass and volume: –If the mass is measured in g and volume in cm3, then the density will be in g/cm3 –If the mass is measured in kg and volume in m3, then the density will be in kg/m3
The volume of an object may not always be given directly, but can be calculated with the appropriate equation depending on the object’s shape
Pressure
Pressure tells us how concentrated a force is, it is defined as the force per unit area p= F/A This equation tells us —If a force is spread over a large area it will result in a small pressure —If it is spread over a small area it will result in a large pressure
The units of pressure depend on the units of area
- If the area is measured in cm2 (and the force in N), then the pressure will be in N/cm2
- If the area is measured in m2 (and the force in N), then the pressure will be in N/m2
- Pressure can also be measured in pascals, Pa where 1 Pa is the same as 1 N/m2 -Pressure, unlike force, is a scalar. Therefore pressure does not have a specific direction
U-tube manometer
A manometer is an instrument to measure pressure and density of two liquids
Hydrostatic pressure
- is the pressure that is exerted by a fluid at equilibrium at a given point within the fluid, due to the force of gravity
- This is when an object is immersed in a liquid, the liquid will exert a pressure, squeezing the object
- The size of this pressure depends upon the density (ρ) of the liquid, the depth (h) of the object and the gravitational field strength (g): ∆p = ρg∆h
When asked about the total pressure remember to also add the atmospheric pressure
-Total pressure = Hydrostatic pressure + Atmospheric pressure -Atmospheric pressure (also known as barometric pressure) is 101 325 Pa
Upthrust
-Upthrust is a force which pushes upwards on an object submerged in a fluid i.e. liquids and gases
- Also known as buoyancy force, upthrust is due to the difference in hydrostatic pressure at the top and bottom of the immersed object
- The force of upthrust is significantly larger in liquids than in gases, this is because liquids are much denser than gases
- Recall that hydrostatic pressure depends on the height (h) or depth that an object is submerged in from P = ρgh -Therefore, the water pressure at the bottom of an object is greater than the water pressure at the top
- Upthrust is a force and is directly proportional to the pressure. The force on the bottom of the can will be greater than the force on top of the can -This resultant pressure causes a resultant upward force on the can known as upthrust
- Upthrust is why objects appear to weigh less when immersed in a liquid. If the upthrust is greater than the weight of the object, the object will rise up
- For an object to float, it must have a density less than the density of the fluid its immersed in
Archimedes’ Principle
-Archimedes’ principle states that an object submerged in a fluid at rest has an upward buoyancy force (upthrust) equal to the weight of the fluid displaced by the object
- The object sinks until the weight of the fluid displaced is equal to its own weight
- Therefore the object floats when the magnitude of the upthrust equals the weight of the object
- The magnitude of upthrust can be calculated by F= pgV F= upthrust (bouyancy force) (N) p= density (kgm^-3) g=gravitional (ms^-1) v= volume displaced(m^3)
Stability
The position of centre of gravity affect its stability -an object is stable when it’s centre of gravity lays above its base -wider the base = lower centre of gravity = more stable -narrower the base = higher centre of gravity = less stable
Centre of gravity vs centre of mass
-centre of mass does not depend on the gravitational field -since weight= mass x gravitational potential energy means that the centre of gravity depends on the gravitational field
