8.3 - terminal speed DO PRACTICAL !

which force does an object moving through a fluid experience?

drag force

what does drag force effect?

any object moving through a fluid

what is a fluid?

liquid or gas

what does the drag force depend on?

• the object’s shape

• the object’s speed

• the fluid’s viscosity

what is the fluid’s viscosity?

a measure of how easily the fluid flows past a surface

what is a measure of how easily a fluid flows past a surface?

the fluid’s viscosity

how does drag force vary with object’s speed through a fluid?

the faster the object travels, the greater the drag force

the faster an object travels in a fluid, the greater / smaller the drag force?

greater

the slower an object travels in a fluid, the greater / smaller the drag force?

smaller

how does the drag force on an object released from rest increase?

it increases as object speed increases

what is the resultant force on an object moving through a fluid?

F_R = m g - drag

• m g = object’s weight

• drag = self explanatory lolz

F_R = m g - drag

resultant force of an object falling through a fluid

why is the resultant force of an object falling through a fluid F_R = m g - drag ?

• downwards is resolved positively, upwards is resolved negatively

• therefore F_R = m g - drag

how does the resultant force of an object falling through a fluid vary with drag?

as drag force increases, the resultant force decreases

as the drag force increases, the resultant force decreases / increases?

as drag force increases, the resultant force decreases

as the drag force decreases, the resultant force decreases / increases?

as drag force decreases, the resultant force increases

why does resultant force decrease as drag force increases?

• object’s weight > drag force because the object is falling

• object’s speed increases the longer it has been falling

• drag force increases with increasing speed

• as weight is constant on earth, it does not vary with increasing speed

• therefore the magnitude of the drag force becomes closer to the magnitude of weight as it increases

• F_R = m g - drag

• therefore resultant force decreases as drag force increases

how does acceleration vary with increasing drag force?

acceleration decreases with increasing drag force

as the drag force increases, the acceleration decreases / increases?

decreases

why does acceleration decrease with increasing drag force?

• newton’s second law states that the acceleration is proportional to and acts in the same direction as the resultant force

• resultant force decreases with increasing drag force, as the drag force becomes closer in value to the object’s weight

• therefore acceleration decreases with decreasing drag force

as resultant force decreases, acceleration increases / decreases?

as resultant force decreases, acceleration decreases?

why does acceleration decrease as resultant force decreases?

• newton’s second law states that the acceleration is proportional to and acts in the same direction as the resultant force

• therefore acceleration decreases as resultant force decreases

what is terminal speed?

when drag force is equal and opposite to weight, so the object falls at a constant velocity with no resultant force or acceleration

what is the drag force acting on an object in terminal speed?

equal and opposite (balanced) to the object’s weight

why is the drag force equal and opposite to the weight when an object is in terminal speed?

because resultant force is zero at terminal speed

what is the resultant force of an object in terminal speed?

zero

why is the resultant force of an object in terminal speed zero?

because the drag force has been increasing as the object’s speed whilst falling increased, and is now of equal magnitude and opposite to the weight. resultant force = weight - drag, so if the forces are balanced, resultant = 0

what is the acceleration of an object in terminal speed?

zero

why is the acceleration of an object in terminal speed zero?

no resultant force (as forces are balanced) = no acceleration

what is the velocity of an object in terminal speed?

constant

why is the velocity constant for an object in terminal speed?

because there’s no resultant force, therefore no acceleration, therefore velocity stays constant

what forces are at play for an object in terminal speed?

here

weight and drag force, which are equal and opposite therefore meaning the forces are balanced and the resultant is zero

what state is an object falling through a fluid in when its drag force is equal and opposite to its weight?

terminal speed

when does an object falling through a fluid reach terminal speed?

when its drag force has increased enough (with increasing object speed) that it is equal and opposite (balanced) to the object’s weight

which objects are capable of reaching terminal speed?

objects falling through a fluid

what is the experiment for investigating terminal speed?

what are the results of the experiment investigating terminal speed?

what do the results of the experiment investigating terminal speed show?

what equipment is used in the experiment investigating terminal speed?

here

how do you find the acceleration on a speed-time curve?

the magnitude of the acceleration at any instant is the gradient

what does the top speed of a vehicle depend on?

• engine power

• shape (streamlined is faster)

for two vehicles of equal engine power, which has the greater top speed - the streamlined vehicle or the non-streamlined vehicle?

the streamlined vehicle

what is the motive force, F_E?

the driving force provided by the engine

why do streamlined vehicles have a higher top speed?

bcuz their curved design manipulates the air’s direction of motion, meaning the vehicle experiences less air resistance, therefore less resistive forces

what forces are at play for a vehicle?

here

• motive force, F_E

• friction and drag forces, F_R

what is the resultant force for a vehicle?

resultant force = F_E - F_R

• F_E = motive force (from engine)

• F_R = resistive forces (sum of drag and frictional forces)

resultant force = F_E - F_R

resultant force for a vehicle

why is the resultant force for a vehicle F_E - F_R?

• driving motion is resolved positively, frictional forces are resolved negatively

• therefore resultant force = F_E - F_R

what does F_R denote?

the total resistive forces (sum of drag and frictional forces) and NOT resultant force like i’ve been doing the whole time !!!

what does F_E denote?

motive force (driving force) provided by the engine

what is the acceleration for a vehicle?

a = (F_E - F_R) / m

• a = acceleration

• F_E = motive force provided by engine

• F_R = total resistive forces

• m = vehicle’s mass

a = (F_E - F_R) / m

acceleration of a vehicle

why is the acceleration of a vehicle a = (F_E - F_R) / m ?

• F = m a

• F = resultant force = F_E - F_R

• F_E - F_R = m a

• rearrange for a

• a = (F_E - F_R) / m

what is terminal speed known as?

maximum speed

can an object’s speed exceed it’s terminal speed?

no

why is terminal speed maximum speed?

there is no acceleration, so the object’s speed cannot increase

is terminal speed a fixed value?

no, because it depends on drag and object’s weight. it is constant for the object in that particular scenario tho

what is the maximum speed (V_max) of a vehicle?

• it’s terminal speed

• F_E = F_R

F_E = F_R

terminal speed for powered vehicles

m g = drag

terminal speed for objects falling through a fluid

when does a vehicle reach V_max?

when the resistive forces becomes equal and opposite (balanced) to the engine force, i.e., when it reaches terminal speed

why does a vehicle reach V_max at terminal speed?

bcuz at terminal speed there is zero acceleration, so there is no way to make the vehicle speed up and velocity is constant

how do hydrofoil boats work?

• they have powerful jet engines as well as their ordinary propeller engine which, when turned on, extends hydrofoils that the boat uses to ski on the water

• the boat speeds up due to the power jet engine, and drag force is reduced as the hull is no longer in the water

• terminal speed (of hydrofoil); F_E of jet engine = drag against hydrofoil

• when the jet engine is switched off, the drag force on the hydrofoils reduce the speed of the boat and the hydrofoils are retracted

• speed drops further until terminal speed (of boat) is reached

• terminal speed (of boat); F_E of propeller engine = drag against boat

• hydrofoil terminal speed > boat terminal speed

why are hydrofoil boats faster (at terminal speed) than ordinary boats?

they have a larger motive force from the more powerful jet engine and experience less drag because their hull is out of the water

what is the terminal speed of a hydrofoil boat when the jet engine and hydrofoils are in use?

F_E of jet engine = drag against hydrofoil

what is the terminal speed of a hydrofoil boat when the jet engine and hydrofoils are not in use?

F_E of propeller engine = drag against boat

why does a hydrofoil have a larger motive force than a regular boat?

because it’s motive force comes from a more powerful jet engine as opposed to the propeller engine on boats

why does a hydrofoil experience less drag forces than a regular boat?

because, when lifted on it’s hydrofoils, the boat’s hull is not in the water so it experiences much less drag (from the fluid) than a boat with a submerged hull would