Physics – Module 1 – Moving About
1. Vehicles do not typically travel at a constant speed
· identify that a typical journey involves speed changes
A typical journey will involve speed changes. This may be slowing down due to getting caught in traffic, speeding up while going downhill, slowing down while turning etc.
· distinguish between the instantaneous and average speed of vehicles and other bodies
The instantaneous speed of any object is the speed at that particular instant of time. Eg. During a 100m race this may be at the 50m point. (Which may be 18.5 m/s)
The average speed of any object is the speed over a period of time, or a distance.
Eg. During a 100m race the average speed of the runner from the starting point to the 50m point may be 10m/s.
The average speed is the total distance traveled divided by the total time taken, whereas the instantaneous speed is just a particular point in time (no other considerations are take such as how far traveled previously).
· distinguish between scalar and vector quantities in equations
There is one main difference between scalar and vector quantities. That is that scalar quantities do not give the direction in which the object is moving, the only give the magnitude. Vector quantities give both direction and magnitude.
Eg. 100m/s – Scalar since there is no direction given (In this case this was speed)
100m/s North East – Vector since there is a direction given (This was Velocity)
Examples of Scalar and Vector quantities:
Speed - Scalar Velocity - Vector
Volume - Scalar Acceleration - Vector
Distance - Scalar Displacement - Vector
Time – Scalar Force – Vector
Distance is the total length travelled by an object from start to stop. It is a scalar quantity.
Displacement is the direct distance from an objects start to stop. It is a vector quantity.
· compare instantaneous and average speed with instantaneous and average velocity
Instantaneous speed is the speed of an object at any particular point in time.
Average speed is the distance traveled during a particular period of time divided by the time itself.
Instantaneous and average speeds are both scalar quantities.
Velocity is a measure of the time rate of displacement. It is a vector quantity.
The instantaneous velocity is the velocity (speed and direction) of an object at a particular point in time.
The average velocity is the total displacement of that object divided by the time period.
For motion in a straight line, the magnitude of the velocity is the same as that for speed.
· define average velocity as:
“r” refers to the total displacement. ‘t’ refers to the total time. This equation is used to finds the average velocity and is the total displacement divided by the time.
Example question:
If a cyclist rides a distance of 6km north and then 8km east in 20 minutes. Determine:
a) Distance traveled
b) Displacement
c) Average speed 8km
d) Average Velocity
Answers:
a) Distance = 6+8 = 14km
b) Displacement using Pythagoras’ theorem: 10km
Direction is given by tan x = 8/6 6km
x = 53.1 degrees x Displacement
Therefore Displacement is 10km north 53.1 degrees East
c) Average Speed = Distance traveled / Time taken:
= 14km / 20 minutes
= 0.7 km/m
d) Average Velocity = Total Displacement / Time:
= 10km North 53.1 degrees East / 20 minutes
= 0.5 km/m North 53.1 degrees East.
· Present information graphically of:
o Displacement vs. time
o Velocity vs. time
o For objects with uniform and non-uniform linear velocity
Displacement-Time “The gradient of a displacement-time graph represents the velocity”
Velocity-Time “The gradient of a velocity-time graph represents acceleration”
“ The displacement of an object during a time interval can be determined by obtaining the area under the graph”
Acceleration-Time
2. An analysis of the external forces on vehicles helps to understand the effects of acceleration and deceleration
· describe the motion of one body relative to another
When the velocity of an object is measured by a moving observer it is referred to as the ‘Relative Velocity’. The equation to the left states that the Velocity of A (object) relative to B (Observer) . Is the velocity of A minus the Velocity of B.
For Example: If you are in car travelling at a constant velocity of 90km/h due west on a straight road, and there is a car ahead of you travelling at 100 km/h due west. Then the relative velocity of that Car:
Relative Velocity = 100 – 90 = 10 km/h due west.
For Example: If you are in car travelling at a constant velocity of 90km/h due west on a straight road, and there is a car ahead of you travelling at 100 km/h due east. Then the relative velocity of that Car:
Relative Velocity = -100 – 90 = -190 km/h due west
= 190 km/h due east
· identify the usefulness of using vector diagrams to assist solving problems
Vector diagrams are useful when trying to solve problems in which objects are moving in different directions. As was seen in the cyclist problem, the use of the Vector diagram allowed us to clearly depict the situation and made solving the problem clearer and simpler.
eg. Find V1/2 = V1 - V2 V1/2 = V1 - V2 = V1 + (-V2)
Note: To subtract Vector 2 from Vector 1. Then Add Vector –2 to Vector 1 (In-Diagram)
· explain the need for a net external force to act in order to change the velocity of an object
Newton’s First Law: “An object will stay at rest or travel at a constant velocity unless acted upon by an external unbalanced force.”
Newtons First Law relates to a concept called Inertia. Inertia is the tendency of an object to resist a change in motion. Inertia is not a force; it is a property of all objects. The inertia of an object depends only on its mass. For example, a larger object travelling at a high speed is harder to stop than a lighter object travelling at the same speed.
This means that in order to change the velocity of an object you need an external unbalanced net force. The vector sum of the forces acting on an object is called the net force.
For example when a car accelerates, the thrust provided by the engine allows to car to overcome the friction applied to it and allows it to change its velocity.
It is difficult to see the law applied on Earth as there are always forces applied on the object on Earth, eg. Air resistance, friction, gravity etc. But in space where there is little external force this law holds true.
Therefore, in a perfect vacuum, unless an object has a force applied on it, it will remain at rest or move in the same direction at the same speed.
· describe the actions that must be taken for a vehicle to change direction, speed up and slow down
In order to speed up, the thrust provided by the engine of the vehicle must exceed the friction that is being applied on the vehicle. I.e. It must have a overall net force in the forward direction.
In order to slow down, the thrust provided by the engine of the vehicle must be less than that of the friction that is applied on the vehicle. This can be done by releasing foot off the accelerator which will result in the gradual slowing down of the vehicle or the brake can be applied which increases the amount of resistance (friction) between the vehicle and the ground, resulting in a more rapid deceleration.
In order to change direction of a vehicle, a external unbalanced force must be applied from one side of the vehicle. Eg. When a car wants to turn right, the steering wheel is turned right which causes more force to be applied on the right side of the car resulting in the car to change direction to the right.
· describe the typical effects of external forces on bodies including:
§ friction between surfaces
§ air resistance
Friction is the resistance (in terms of motion) between the surfaces of two objects. It decelerates that object.
Air resistance acts in the opposite direction of motion to an object and also decelerates it.
Gravity (Weight) is the force that pulls all bodies towards the ground. It has no obvious affect on most objects, but on objects that need to move upwards such as rockets, gravity poses as a significant resistance to them.
Normal Reaction force is a force that acts perpendicular to a surface as a result of an object applying a force to the surface. For example when you walk, to exert force onto the ground and there is a normal reaction force which is exerted onto your foot. The magnitude of both forces is the same.
Driving force (Thrust): The thrust is simply the forward force applied on a body which causes it to accelerate.
· define average acceleration as:
The rate at which an object changes its velocity is called its ACCELERATION. Acceleration is a Vector quantity.
The ‘v’ refers to change in velocity. The change in velocity is equal to the ending velocity minus the initial velocity which gives us the second equation.
· define the terms mass and weight with reference to the effects of gravity
Your mass will not change if you change locations, no matter where you go. If you have 50kg of mass on the Earth. Your will have 50kg of mass on the Moon as well.
It is your weight that will change.
W=mg
W refers to weight
M refers to mass
G refers to the force of gravity. (gravitational field strength)
On Earth the force of gravity is approximately 9.8 N
Therefore to determine your weight on Earth, you multiply your mass by the gravitational field strength (9.8).
· outline the forces involved in causing a change in the velocity of a vehicle when:
§ coasting with no pressure on the accelerator
§ pressing on the accelerator
§ pressing on the brakes
§ passing over an icy patch on the road
§ climbing and descending hills
§ following a curve in the road
Coasting with no pressure on the accelerator: In theory if this was the case, you should move at a constant velocity eternally but on Earth this is not true as there are several resistance factors that cause the car to slow down and eventually come to rest. Air resistance and friction are the two major components. Friction between the tyres and the road as well as the air resistance on the vehicle cause it to eventually come to a halt. Thus the velocity is always decreasing.
If the car was to move at a constant velocity, then the thrust provided by the engine should be equal to the resistance applied by the friction and the air resistance. This will result in a overall net force of 0 and thus you would coast along at a constant velocity.
Pressing on the accelerator: This will result in a force to applied by the engine. The thrust applied by the engine will exceed the friction and air-resistance factors and cause the vehicle to increase it’s velocity accordingly (accelerating). Simply, when the accelerator is pressed a force is applied on the road by the wheels of the car, and due to Newton’s third law, we know that there will be an equal and opposite reaction force and this is the force that causes the vehicle to accelerate.
Pressing on the brakes: When the brakes are pressed, the engine produces a force which causes the wheels to stop turning (or turn slower). This increases the frictional forces that are applied on the car as well as reduces the thrust that is applied by the engine. Due to both of these factors, the car’s velocity will reduce. Thus the care will decelerate (or accelerate in a negative direction).
Passing over an icy patch on the road: Let us assume that the car is travelling at a constant velocity (i.e. no net force). An icy patch on the road will apply less friction onto the car than a normal bitumen-based road will. Due to this fact, as the car gets onto the icy patch and keeps the same pressure on the accelerator, it will travel faster (accelerate) as the frictional forces have been reduced, which means that there is a net force in the direction the car is travelling. This causes increases in velocity and causes the car to accelerate.
Also, due to the fact that the icy road provides minimal friction to that of the normal road, it will be difficult for the vehicle to reduce it’s velocity. This is because as the brakes are applied, the deceleration of the car relies on the frictional forces between the wheels and the road and since there are minimal frictional forces, it will be hard to car to slow down.
Climbing and Descending Hills:
It is important in these scenarios to split up the several forces into their components.
In the diagram to the right. The angle of inclination is always equal to the angle of between the normal and the force of gravity. As can be seen there is a net force applied in the downhill direction. This force can be calculated if the mass of the object is known. The normal reaction force is always perpendicular to the surface and this can be seen in both scenarios. Friction and air resistance play important roles in restricting the movement of the object and the amount of force needed is dependant on if you are travelling uphill or down hill.
In the diagram to the left, in order to accelerate the car, the driving force must be greater than the sum of the frictional force, air resistance and the downhill force (weight component parallel to surface) applied on the car. These three forces are acting in an opposite direction to the direction of the car. Thus this shows why more force is needed to travel uphill, rather than downhill.