7.7 + 7.8 - projectile motion

what’s a projectile?

• any object that is acted upon only by the force of gravity

• any form of motion where an object experiences a constant acceleration in a different direction to its velocity

what is similar between a projectile and an object in free fall?

they are both acted on only by the force of gravity

what is different between a projectile and an object in free fall?

• projectile motion has both vertical and horizontal movement, an object in free fall only has vertical motion

• projectile motion experiences constant acceleration in a different direction to its velocity, which does not occur in free fall because there is only one direction of motion in free fall

which has both vertical and horizontal motion - a projectile or an object in free fall?

projectile

which has only vertical motion - a projectile or an object in free fall?

object in free fall

what are the key principles of a projectile?

1. acceleration always equal to g and is always downwards, therefore no horizontal acceleration

2. horizontal velocity is constant because there is no horizontal acceleration

3. horizontal and vertical motions are independent of each other

what is acceleration in projectile motion?

• vertical acceleration = g, + 9.81 ms^-2

• horizontal acceleration = 0

what is the vertical acceleration in projectile motion?

equal to g, 9.81 ms^-2

is vertical acceleration positive or negative?

positive

why is vertical acceleration positive?

because it always acts downwards

what is the horizontal acceleration in projectile motion?

zero

does acceleration affect horizontal or vertical motion?

only vertical

why does acceleration only affect vertical motion?

because there is no horizontal acceleration in projectile motion

which has a constant velocity - vertical or horizontal motion?

horizontal motion

why does horizontal motion have a constant velocity?

because there is no horizontal acceleration

is vertical velocity constant?

no

is horizontal velocity constant?

yes

why isn’t vertical velocity constant?

because there is vertical acceleration

are the motions of vertical and horizontal motion independent?

yes

do the motions of vertical and horizontal motion affect each other?

no

why don’t the motions of vertical and horizontal motion affect each other?

because they are independent of each other

when released from a cliff, what affects the object’s horizontal distance?

the initial speed the object is projected

when released from a cliff, does the time affect an object’s horizontal distance?

no

what is the path taken for an object thrown off a cliff?

here

curved path through the air that become steeper as it drops

what affects the horizontal distance of an object projected off a cliff?

the velocity of its projection (initial velocity)

what doesn’t affect the horizontal distance of an object projected off a cliff?

the time taken for the object to fall

how can SUVAT equations be rewritten when dealing with projectiles or objects in free fall?

with the symbol ‘g’ replacing ‘a’

why, in SUVAT equations dealing with projectiles or objects in free fall, can ‘a’ be substituted for ‘g’?

the only acceleration in projectile motion is vertical, and the only force acting on projectiles is the force of gravity, therefore acceleration can be substituted for gravitational field strength

which falls faster - an object projected horizontally or an object in free fall?

they both fall at the same speed

why do objects projected horizontally and objects in free fall fall at the same speed?

there is no horizontal acceleration in projectile motion, and vertical acceleration is gravitational field strength for both projectiles and objects in free fall, therefore both accelerate at the same rate and therefore fall with the same speed

how can projectile motion be investigated?

using a stroboscope and a camera with a slow shutter speed (or video camera) to record the motion of a projectile in comparison to the motion of an object in free fall

here

what equipment is used to investigate projectile motion?

• stroboscope

• camera with slow shutter speed, or video camera

• 2 balls falling, one projected horizontally the other in free fall

what does the investigation of projectile motion using a stroboscope show you about a projectile’s horizontal motion?

that it changes by equal distances between successive flashes, meaning the horizontal component of the projectile’s motion is constant and therefore there must be no horizontal acceleration

here

how does the investigation of projectile motion using a stroboscope prove there is no horizontal acceleration?

the position of the projectile changes by equal distances between successive flashes, meaning the horizontal component of the projectile’s motion is constant and therefore there must be no horizontal acceleration

here

how does the investigation of projectile motion using a stroboscope prove that horizontal velocity is constant?

the position of the projectile changes by equal distances between successive flashes, meaning the horizontal component of the projectile’s motion is constant and therefore there must be no horizontal acceleration

here

what does the investigation of projectile motion using a stroboscope show you about a projectile’s vertical motion?

here

the vertical position of the projectile changes at the same rate as the object falling in free fall, therefore the projectile’s vertical acceleration is the same as the object in free fall, which is g

how does the investigation of projectile motion using a stroboscope prove that acceleration of a projectile is the gravitational field strength?

the vertical position of the projectile changes at the same rate as the object falling in free fall, therefore the projectile’s vertical acceleration is the same as the object in free fall, which is g. since there is no horizontal acceleration, the acceleration of the projectile is g

here

what is the horizontal component of an object projected horizontally?

x = u t

here

what is the vertical component of this object projected horizontally?

y = ½ g t²

here

how do we denote horizontal motion?

x

what does x denote?

horizontal motion

how do we denote vertical motion?

y

what does y denote?

vertical motion

why is the horizontal component of an object projected horizontally x = u t?

• s = u t + ½ a t²

• there is no horizontal acceleration

• s = u t + ½ (0) t²

• therefore x = u t, following the equation distance = speed x time as speed is constant with no horizontal acceleration

why is the vertical component of an object projected horizontally y = ½ g t² ?

• s = u t + ½ a t²

• the initial vertical velocity is 0, why?

• s = (0) t + ½ a t²

• s = ½ a t²

• vertical acceleration is g

• therefore y = ½ a t²

why is the initial vertical velocity of an object projected horizontally zero?

because its projected horizontally idiot. it hasn’t started falling yet

what is the horizontal component of velocity for an object projected horizontally?

V_x = u

V_x = u

the horizontal component of velocity for an object projected horizontally

what is the vertical component of velocity for an object projected horizontally?

V_y = - g t

why is the horizontal component of velocity for an object projected horizontally V_x = u ?

there is no horizontal acceleration so horizontal velocity stays constant

V_y = - g t

the vertical component of velocity for an object projected horizontally

why is the vertical component of velocity for an object projected horizontally V_y = - g t ?

what is the speed at any point on the path of an object moving with horizontal projection?

(v²_x + v²_y)^1/2

(v²_x + v²_y)^1/2

the speed at any point on the path of an object moving with horizontal projection

why is the speed at any point on the path of an object moving with horizontal projection (v²_x + v²_y)^1/2 ?

what is parabolic?

a curve formed from an object thrown in the air that lands in a different place

what are examples of parabolic projectile motions?

• a ball rolling on an inclined board

• c

what is a ball rolling on an inclined plane an example of?

a parabolic projectile motion

what is the path of a beam of electrons directed between two oppositely charged parallel plates an example of?

a parabolic projectile motion

why is a ball rolling across an inclined board an example of parabolic projectile motion?

• the ball moves at constant acceleration and ends it motion in a different place to where it started

• the ball’s velocity acts across the board yet it’s acceleration acts downwards into the board, meaning acceleration is experienced in a different direction to velocity

here

why is the path of a beam of electrons directed between two oppositely charged parallel plates an example of parabolic projectile motion?

• the negatively charged electron experiences a constant force attracting it to the positively charged plate, meaning the electron experiences constant acceleration

• the electron’s velocity has horizontal and vertical components, yet its acceleration parallel to the plate is zero while its acceleration perpendicular to the plate is constant, therefore the electron experiences constant acceleration in a different direction to its velocity

• the electron ends its motion in a different place to where it started, meaning it has parabolic motion

here

describe the path of a ball rolling across an inclined board

projected across the top of the board from the side. its path curves down the board and is parabolic

describe the path of a beam of electrons directed between two oppositely charged parallel plates

each negatively charged electron in the beam is acted on by a constant force towards the positively charged plate, therefore the electron experiences constant acceleration towards the plate and moves with parabolic motion as its acceleration parallel to the plate is zero and its acceleration perpendicular to the plate is constant, and because it finishes its motion in a different place to where it started

here

what is drag force / air resistance?

a force that drags on a projectile moving through the air because of the resistance of the air

what affects a projectile moving through the air?

drag force / air resistance

what is drag due to?

• resistance of the air

• partly caused by the friction between the layers of air near the projectile’s surface where the air flows over the surface

what does the resistance of the air cause?

a drag force against a projectile moving through the air

what does the friction between layers of air near the projectile’s surface where the air flows over the surface cause?

a drag force against a projectile moving through the air

what are the characteristics of drag force?

• acts in the opposite direction to the direction of motion of the projectile

• increases as the projectile’s speed increases

• is a horizontal component that reduces both the horizontal speed of the projectile and its range

• reduces the maximum height of the projectile if its initial direction is above the horizontal and makes its descent steeper than its ascent

what can affect a projectile’s maximum height?

drag, if the projectile’s initial direction is above the horizontal and makes it descent steeper than its ascent

when can drag affect a projectile’s maximum height?

if the projectile’s initial direction is above the horizontal and makes it descent steeper than its ascent

what happens when the projectile’s initial direction is above the horizontal and makes it descent steeper than its ascent?

drag force will affect the projectile’s maximum height

what direction does drag act in?

• the opposite direction to the direction of motion of the projectile

• horizontally

what acts in the opposite direction to the direction of motion of the projectile?

drag force

what increases drag force?

increased projectile speed

what decreases drag force?

decreased projectile speed

what does increased projectile speed cause?

increased drag

what does decreased projectile speed cause?

decreased drag

is drag force horizontal or vertical?

horizontal

what does drag reduce in a projectile?

• the projectile’s horizontal speed

• the projectile’s range (horizontal distance)

what affects a projectile’s horizontal speed?

drag

what affects a projectile’s range (horizontal displacement)?

drag

what is height?

vertical displacement

what is range?

horizontal displacement

what is vertical displacement?

height

what is horizontal displacement?

range

what is lift force?

the upwards force of an object moving through a fluid (such as air)

when can lift force affect a projectile?

depending on the projectile’s shape - if the projectile’s shape causes the air to flow faster over the top of the object than underneath it

what does a projectile’s shape affect?

• the drag force

• whether or not a projectile will experience lift force

why does a projectile’s shape determine whether or not the projectile will experience lift?

if the projectile’s shape causes the air to flow faster over the top of the object than underneath it, the pressure of the air on the top surface is less than the one on the bottom surface, and this pressure difference causes a lift force on the object

what affects drag?

• projectile’s speed

• projectile’s shape

what happens if the projectile’s shape causes the air to flow faster over the top of the object than underneath it?

the pressure of the air on the top surface is less than the one on the bottom surface, and this pressure difference causes a lift force on the object

what force does a spinning ball experience?

a force due to the same effect as the lift force, except this force can be downwards, upwards, or sideways, depending on how the ball is made to spin

what object experiences a force due the same effect as lift force?

a spinning ball

what are the similarities between a projectile experiencing a lift force and a spinning ball?

they both experience a both due the same effect (differences in air flow velocity causing a pressure difference)

what are the differences between a projectile experiencing a lift force and a spinning ball?

the lift force experienced by a projectile is always upwards, whilst the force acting on a spinning ball can be downwards, upwards, or sideways, depending on how the ball is spun

what direction is the force experienced by a spinning ball due to?

how the ball is spun

what does the way a spinning ball is spun affect?

the direction of the force experienced by the spinning ball

what would be the motion of a projectile if there were no gravity or air resistance?

a straight line with no change in velocity

when would a projectile move in a straight line with no change in velocity?

if there were no gravity or air resistance