Chapter 3 Dynamics

Question 1

What is Mass?

Answer 1

• Mass is the measure of the amount of matter in an object
• Consequently, this is the property of an object that resists change in motion
• The greater the mass of a body, the smaller the change produced by an applied force
• The SI unit for mass is the kilogram (kg)

Question 2

Weight

Answer 2

• is the effect of a gravitational field on a mass
• Since it is a force on an object due to the pull of gravity, it is measured in Newtons (N) and is a vector quantity
• The weight of a body is equal to the product of its mass (m) and the acceleration of free fall (g)
• g is the acceleration due to gravity or the gravitational field strength
• On Earth, this is 9.81 m s−2 (or N kg−1)

Question 3

Mass v Weight

Answer 3

• An object’s mass always remains the same, however, its weight will differ depending on the strength of the gravitational field on different planets

Question 4

Force & Acceleration

Answer 4

• As stated on the previous page, Newton’s Second Law of Motion tells us that objects will accelerate if there is a resultant force acting upon them
• This acceleration will be in the same direction as this resultant force F= Mg

Question 5

Resultant Force

Answer 5

• Since force is a vector, every force on a body has a magnitude and direction
• The resultant force is therefore the vector sum of all the forces acting on the body. The direction is given by either the positive or negative direction as shown in the examples below
• The resultant force could also be at an angle, in which case addition of vectors is used to find the magnitude and direction of the resultant force.

Question 6

Acceleration

Answer 6

• Given the mass, Newton’s Second Law means you can find the acceleration of an object
• Since acceleration is also a vector, it can be either positive or negative depending on the direction of the resultant force
• Negative acceleration is deceleration -An object may continue in the same direction however with a resultant force in the opposite direction to its motion, it will slow down and eventually come to a stop

Question 7

Newton’s First Law:

Answer 7

A body will remain at rest or move with constant velocity unless acted on by a resultant force

Question 8

Newton’s Second Law:

Answer 8

• A resultant force acting on a body will cause a change in momentum in the direction of the force.
• The rate of change in momentum is proportional to the magnitude of the force
• -This can also be written as F = ma

Question 9

Newton’s Third Law:

Answer 9

• If body A exerts a force on body B, then body B will exert a force on body A of equal magnitude but in the opposite direction
• Newton’s Third Law force pairs must act on different objects
• Newton’s Third Law force pairs must also be of the same type e.g. gravitational or frictional

Question 10

Linear Momentum

Answer 10

• Linear momentum (p) is defined as the product of mass and velocity
• P= mv
• p= momentum (kgms^-1)
• m= mass (kg)
• v=velocity(ms^-1)

Question 11

Momentum is a vector quantity

Answer 11

• it has both a magnitude and a direction -This means it can have a negative or positive value
• If an object travelling to the right has positive momentum, an object travelling to the left (in the opposite direction) has a negative momentum
• The SI unit for momentum is kg m s−1

Question 12

Force & Momentum

Answer 12

• Force is defined as the rate of change of momentum on a body
• Force is equal to the rate of change in momentum
  
  • The change in momentum is defined as the final momentum minus the initial momentum:
    
    • pfinal − pinitial
      
      • Force and momentum are vectors so they can be either positive or negative values

Question 13

Force is equal to the rate of change in momentum

Answer 13

Question 14

Direction of Forces

Answer 14

• The force that is equal to the rate of change of momentum is still the resultant force
• A force on an object will be negative if it is directed in the opposite motion to its initial velocity.
• This means that the force is produced by the object it has collided with

Question 15

Maths tip

Answer 15

• ‘Rate of change’ describes how one variable changes with respect to another. In maths, how fast something changes with time is represented as dividing by Δt (e.g. acceleration is the rate of change in velocity)
• More specifically, Δt is used for finite and quantifiable changes such as the difference in time between two events

Question 16

Drag Forces

Answer 16

• Drag forces are forces acting the opposite direction to an object moving through a fluid (either gas or liquid)
• Examples of drag forces are friction and air resistance
• A key component of drag forces is it increases with the speed of the object.

Question 17

Air Resistance

Answer 17

• Air resistance is an example of a drag force which objects experience when moving through the air
• Air resistance depends on the shape of the body (object) and the speed it’s travelling
• Since drag force increases with speed, air resistance becomes important when objects move faster

Question 18

Terminal Velocity

Answer 18

• For a body in free fall, the only force acting is its weight and its acceleration g is only due to gravity.
• The drag force increases as the body accelerates
• This increase in velocity means the drag force also increases
• Due to Newton’s Second Law, this means the resultant force and therefore acceleration decreases (recall F = ma)
• When the drag force is equal to the gravitational pull on the body, the body will no longer accelerate and will fall at a constant velocity

-This velocity is called the terminal velocity

Question 19

The Principle of Conservation of Momentum

Answer 19

The principle of conservation of momentum is:

• The total momentum of a system remains constant provided no external force acts on it
  
  • For example if two objects collide:
  • the total momentum before the collision = the total momentum after the collision
• Remember momentum is a vector quantity. This allows oppositely-directed vectors to cancel out so the momentum of the system as a whole is zero

-Momentum is always conserved over time

Question 20

External forces

Answer 20

are forces that act on a structure from outside e.g. friction and weight

Question 21

Internal forces

Answer 21

• are forces exchanged by the particles in the system
  e. g. tension in a string Which forces are internal or external will depend on the system itself

Question 22

One-dimensional momentum problems

Answer 22

• Momentum (p) is equal to: p = m × v
• Using the conversation of linear momentum, it is possible to calculate missing velocities and masses of components in the system.

Question 23

To find out whether a collision is elastic or inelastic, compare the kinetic energy before and after the collision

Answer 23

• If the kinetic energy is conserved, it is an elastic collision
• If the kinetic energy is not conserved, it is an inelastic collision

Question 24

Elastic collisions

Answer 24

are commonly those where objects colliding do not stick together and then move in opposite directions

Question 25

Inelastic collision

Answer 25

are where objects collide and stick together after the collision

Question 26

Two-dimensional momentum problems

Answer 26

* Since momentum is a vector, in 2D it can be split up into its x and y components

Question 27

You may also come across a system with no external forces being described as a ‘closed’ or ‘isolated’ system

Answer 27

* These all still refer to a system that is not affected by external forces

Question 28

Elastic Collisions further

Answer 28

* When t**wo objects collide, they may spring apart retaining** all of their kinetic energy. * This is a **perfect elastic collision** * An elastic collision is one where **kinetic energy is conserved** * Since kinetic energy depends on the speed of an object, in a perfectly elastic collision (head-on approach) * **the relative speed of approach = the relative speed of separation**

Question 29

Inelastic Collisions further

Answer 29

* Whilst the **momentum of a system is always conserved** in interactions between objects, kinetic energy may not always be * An inelastic collision is one where kinetic energy is not conserved -The kinetic energy is transferred into other forms of energy such as a heat or sound * **Inelastic collisions can be when two objects collide and they crumple and deform**. Their kinetic energy may also **disappear** completely as they come to a halt * A perfectly inelastic collision is when **two objects stick together after collision**