Projectile Motion

Question 1

Projectile motion (definition)

Projectile (definition)

Answer 1

Movement of a body through the air following a curved flight path under the force of gravity

A body that is launched into the air losing contact with the ground surface such as discuss or long jumper

Question 2

The horizontal distance travelled by a projectile is affected by three factors:

What are they (including small explanation)

Answer 2

Angle of release

• The optimum angle is dependant upon release height and landing height

Speed of release

• Due to Newton’s 2nd Law the horizontal distance a projectile travels is primarily affected by speed of release.
• Greater the velocity of a projectile the greater the horizontal displacement travelled

Height of release

• A greater height results in an increased in horizontal displacement as gravity is acting on a mass.

Question 3

Parabolic flight path (definition)

Parabolic flight path occurs when…

Example

Answer 3

A flight path symmetrical about its highest point caused by the dominant weight force of a projectile

Weight is the dominant force
Means air resistance is small.

The shot put has a high mass and travels through the air at a low velocity, with a relative small frontal cross-sectional area and a smooth surface

Question 4

Non-parabolic flight path (definition)

A non-parabolic flight path occurs when…

Example

Answer 4

A flight path asymmetrical about its highest point caused by the dominant weight force of air resistance

Air resistance is the dominant force

A badminton shuttle has a very low mass and travels at high velocities with a relative uneven surface; this causes an increase in air resistance, and causes the shuttle to fly in a non-parabolic flight path

Question 5

Parabola (definition)

Answer 5

A uniform curve that is symmetrical about it highest point

Question 6

Free body diagrams

These are simple sketches to give a snapshot of the forces acting upon the projectile at a specific time. It demonstrates: (4)

There are 3 phases when drawing the diagram:

Key points to remember:

Answer 6

• which forces are acting
• where they originate from
• relative sizes
• direction in which they are acting

1. Start of flight
2. Mid flight
3. End of flight

a. Weight will not change during these phases
b. Air resistance WILL change as it is dependent upon velocity

Question 7

Free body diagram - Shot put vs Shuttlecock

Answer 7

Question 8

Parallelogram of forces (definition)

How to draw a parallelogram of forces (4 steps)

What does a parallelogram of forces look like (diagram)

Answer 8

A parallelogram illustrating the theory that a diagonal drawn from the point where forces are represented in size and direction shows the resultant force acting

1. On the shot put indicate where the COM of the projectile is
2. Add in the air resistance line and weight (remember to show the direction and which is the dominant force)
3. Add broken parallel lines to weight and air resistance to create a parallelogram
4. Draw a diagonal line from the COM to the opposite corner with a double arrow and label it ‘resultant force’

Question 9

Resultant Force (definition)

What it means
Possible outcomes of resultant forces (2)

Answer 9

The sum of all forces acting on a body or the net force acting on a projectile

A resultant force shows the acceleration of a projectile and the direction in which the acceleration occurs. It will also indicate the flight path

• if the resultant force is close to the weight arrow, weight is more dominant, so the flight path is more parabolic
• if the resultant force is closer to the air resistance arrow, air resistance is more dominant, so flight path will be non-parabolic

Question 10

Parallelogram of forces - Shuttlecock

Answer 10

Question 11

The Bernoulli principle (2 parts)

Lift forces are important as … (2 parts)

Answer 11

• is the creation of an additional lift force on a projectile in flight
• the higher the velocity of air flow, the lower the surrounding pressure.

the overall effect of additional lift is that there is an increased amount of time the projectile hangs in the air;

• which will extend the flight path and the horizontal distance covered.

Question 12

Bernoulli Principle - Aerofoils - What is it?

The science behind it - aerofoils (5)

Answer 12

An aerofoil has a curved upper surface and a flat underneath surface

• When there is a projectile in the air, the air flow is forced to part, however, it needs to meet at the end of the projectile at the same time.
• The curved upper surface of the aerofoil means that air has a further distance to travel; whilst the flat underneath surface has less of a distance to travel
• This means that the velocity over the upper curved surface needs to be higher.
• As velocity increases pressure decreases.
• As all fluids move from an area of high pressure to an area of low pressure, a pressure gradient is formed which results in a lift force.

Question 13

Bernoulli Principle – Lift Force (definition)

As well as having upward lift forces it is possible to have what is known as downward lift force. An example of this is…

Bernoulli Principle - Key terms – Angle of Attack

Answer 13

An additional force created by a pressure gradient forming on opposing surfaces of an aerofoil moving through fluid

This will work if the aerofoil shape is inverted, this is used in F1 cars and track cycling. By increasing the downward force the car and bike are held onto the track at high speeds around corners.

The most favourable angle of release for a projectile to optimise lift force due to the Bernoulli principle

Question 14

Practical example of aerofoils - f1 car (5)

Answer 14

Front wing funnels air down through the narrow space underneath the car’s chassis

The spoiler acts as an inverted aerofoil, forcing air underneath to travel a further distance

Air velocity underneath the car is increased, creating areas of low pressure

A pressure gradient is formed, additional downward lift force is created

The result is increased grip and friction around corners at high speeds

Question 15

Magnus effect (definition)

Answer 15

Creation of an additional Magnus force on a spinning projectile which deviates from the flight path

Question 16

How spin is created?

Four types of spin?

Answer 16

It is created by applying an eccentric force outside the COM. Where the eccentric force is applied will determine the way the projectile spins there are four types:

Topspin

• Eccentric force applied above centre of mass
• Spins downwards around the transverse axis

Backspin

• Eccentric force applied below centre of mass
• Spins upwards around the transverse axis

Sidespin hook

• Eccentric force applied right of the centre of mass
• Spins left around the longitudinal axis

Sidespin slice

• Eccentric force applied left of the centre of mass
• Spins right around the longitudinal axis

Question 17

The way the projectile spins determines: (3)

Answer 17

• The direction
• The velocity
• The pressure of air flow around it

Question 18

A pressure gradient is formed either side of the spinning projectile and an additional Magnus force is created which deviates the flight path. The deviation means all forms of spin create a …

Answer 18

non-parabolic flight path.

Question 19

The effect of the different spins on the flight path (3)

Answer 19

Topspin - Creates a downward Magnus force, shortening the flight path

Backspin - Creates an upward Magnus force, lengthening the flight path

Sidespin - Creates a Magnus effect to the right (slice) and left (hook), swerving the projectile right (slice), and left (hook)

Question 20

Practical example - Magnus force - topspin tennis

For a ball with topspin, the additional Magnus force is created by:

Answer 20

1. The upper surface of the ball rotating towards the oncoming air flow(top to bottom), which opposes motion, decreasing velocity of air flow and creating a higher pressure zone
2. The lower surface of the ball is rotating in the same direction as the air flow, increasing the velocity of air flow and creating a zone of low pressure
3. A pressure gradient is formed and an additional Magnus force being created downwards.

The downward Magnus force adds to the weight of the projectile, the effect of gravity is increased and the projectile ‘dips’ in flight, giving less time in the air as the flight path shortens.

Question 21

Use of spin in golf and football - Hook (5) and Slice (5)

Answer 21

HOOK:

• Air flow opposes motion
• Ball rotates to the left, guiding air flow (high velocity/low pressure)
• Ball rotates against air flow on the right side, resisting air flow(low velocity/high pressure)
• Pressure gradient is formed
• Magnus effect act to deviate flight path to the left

SLICE:

• Air flow opposes motion
• Ball rotates to the right guiding air flow (high pressure/low velocity)
• Ball rotates against air flow on the left side, resisting air flow (low velocity/ high pressure)
• Pressure gradient is formed
• Magnus force act to deviate the flight path to the right

Question 22

Air flow diagram - Topspin

Answer 22

Question 23

Flight path diagram - Topspin

Answer 23

Question 24

Air flow diagram - Hook

Answer 24

Question 25

Flight path diagram - Hook

Answer 25

Question 26

Air flow diagram - Sidespin slice

Answer 26

Question 27

Flight path diagram - Sidespin slice

Answer 27