#### What is being taught lesson by lesson:

This is a huge topic and may be split into several sections by your teacher. For the purposes of this site and revision, I have put everything together.

- Scaler and vector quantities.
- Contact and non-contact forces.
- Gravity and gravitational field strength.
- Resultant forces and vector diagrams.
- Work done and calculating the energy transfer.
- Forces and elasticity. Springs including energy stored in a stretched spring.
- Pressure in fluids.
- Atmospheric pressure.
- Describing motion, distance and displacement.
- Speed and velocity.
- Acceleration.
- Distance-time and velocity time graphs.
- Terminal velocity. This links acceleration and resolution of forces.
- Newton’s 1st law.
- Newton’s 2nd law.
- Newton’s 3rd law.
- Forces involved in braking – deceleration.
- Stopping distances and reaction time/conditions of car and road.

#### Key Terms for this topic (Tier 3 vocabulary)

Vector – scalar – gravitational – resultant – elastic deformation – limit of proportionality – displacement (distance) – velocity – uniform acceleration – terminal velocity – equilibrium – momentum – conservation of momentum.

Forces

Are you ready for your assessment in this topic? Try out this simple quiz.

#### What everyone needs to know:

Scaler quantities only have a magnitude (the dog ran at a speed of 5m/s) whereas vector quantities have both a magnitude and a direction (the dog ran at 5 m/s in a westerly direction). When drawing vectors, we tend to draw and arrow (direction) and the length of the arrow depicts the magnitude. Distance is a scalar quantity, displacement is a vector quantity, it has distance (magnitude) and a direction.

Forces are vector quantities and they can be either contact or non-contact. Contact forces physically touch (friction) whereas non-contact have no touching (gravitational attraction or magnetic forces).

Weight is a vector quantity as you have a weight (magnitude) and it always pulls towards the centre of the earth (direction). Weight can be calculated using your mass and the gravitational field strength where you are (on Earth it is 9.8 N/kg). The mass and weight of an object appears to all act from one point, this is the centre of mass.

Weight (N) = Mass (kg) x Gravitational field strength (N/kg) or W=mg

When more than one force are acting on a body, they can partially or totally cancel each other out. The overall force left over is the resultant force. You need to calculate these, e.g. 5 N pulling left and 8 N pulling right gives a resultant force of 8 – 5= 3N pulling to the right.

Work done is the energy transferred when moving an object, it can be calculated using this founula:

Work done (J) = Force (N) x Distance (m) or W=Fs

You need to describe these energy changes. If there is more friction between the surface the object is on and the object, the force will need to be higher so the work done will be higher. The extra energy will be transferred to heat because of the extra friction.

When forces are applied to objects, they do not all move, some are forced to distort, bend, compress or stretch. Extension of a spring is directly proportional to the force, if the force doubles, the length of the extension doubles. As long as the spring has not passed its elastic limit (returns to original size/shape when the force is removed), we can measure how much it will extend per Newton based on a spring constant:

Force (N) = Spring constant (N/m) x Extension (m) or F = k e

You need to be able to describe the relationships between the three components of this equation and interpret data and graphs. You can also calculate the energy stored in a stretched spring using this equation:

Elastic potential energy (J) = ½Spring constant (N/m) x extension^{2} (m)

E_{e} = ½ke^{2}

Required practical 18 – Investigate the relationship between the force applied to a spring and its extension.

As speed uses distance to calculate it, speed is a scalar quantity. Speeds are almost always changing in cars, bikes or even us walking. It is useful to have a rough idea of speeds, you walk between 1 and 2 m/s and may run up to 3 m/s and on you bike, you may reach 6 m/s. The speed limit for cars in the town is 30 mph which equates to 13.4 m/s whereas the soundwaves coming off a car which allows you to hear it travels at about 330 m/s.

You need to calculate speed, distance and time by using the equation below and rearranging it as needed.

Distance travelled (m) = Speed (m/s) x Time (s) or S = vt

Velocity is a vector quantity so although you can calculate it the same as speed, it must have a single direction.

Using a graph of distance (y-axis) against time (x-axis), you can calculate the speed of an object as the gradient of the line.

You can calculate the average acceleration of an object using this formula:

Acceleration (m/s^{2}) = change in velocity (m/s) / time taken (s)

Another way to calculate this is using a velocity-time graph. The gradient of this graph is equal to the acceleration. You need to be able to draw velocity-time graphs from data or interpret the graphs to obtain data.

For uniform acceleration, you can use the following equation;

Final velocity^{2} (m/s) – Initial velocity^{2} (m/s) = 2 x acceleration (m/s^{2}) x distance (m)

v^{2} – u^{2} = 2 a s

The acceleration due to gravity on Earth is 9.8 m/s^{2}. This is an example that you could use to calculate the final velocity of an object falling to the ground. In reality, the air resistance acting on a falling object increases as its velocity increases. At some point, the air resistance (N) will equal the weight of the falling object (N) and they will cancel out giving a resultant force of 0 N. At this point, there will be no more acceleration.

Newton’s 1st law of motion. If the resultant force on a body is zero, a stationary body will remain stationary whereas a moving body will continue to move at the same velocity. A resultant force is needed to change velocity.

Newton’s 2nd law of motion. The acceleration of an object is proportional to the resultant force. Bigger force = bigger acceleration. This is calculated using this equations:

Force (N) = Mass (kg) x Acceleration (m/s^{2}) or F=ma

Required practical 19 – Investigate how varying the force on an object affects the acceleration when the object’s mass is constant. See how the acceleration is affected by keeping the force the same but varying the mass of the object.

Newton’s 3rd law. When two objects interact, they exert equal and opposite forces on each other. You need to be able to apply this to equilibrium situations.

Overall stopping distance for a car is equal to the thinking distance (distance covered between seeing the hazard and applying the brake) plus the braking distance (the distance covered while the brake is applied until the car comes to a stop). Please note that i have been very careful to state “distance”, don’t quote times – just distances. The faster the car, the longer the overall stopping distance.

Thinking distance is affected by reaction time. Your braking distance will increase due to tiredness, use of drugs or alcohol.

Braking distance will increase if the car’s tyres have low tread or the air pressure is at an incorrect level, the road is wet, icy, covered in mud or has loose gravel. Be prepared to calculate distances based on equations above and link to acceleration and then to braking force.

Larger decelerations need a greater force and these rapid decelerations are dangerous as brakes can overheat and become much less effective or the car can lose control.

#### Extra topics needed for the Higher papers:

You should be able to describe the forces acting on a stationary body and use free body diagrams to show how several forces can lead to one resultant force.

Single forces can be split into two component forces that add up (taking vector directions into account) the single force. You need to resolve forces using vector diagrams.

If a dog runs around in a circle at 4 m/s, its speed is 4 m/s but its velocity is 0 m/s. This is because the direction is constantly changing so there is no velocity.

On a distance-time graph, if an object is accelerating, the line becomes a curve. You can work out the speed at any point on the curve by drawing a tangent and working out the gradient of this tangent.

On a velocity-time graph, the area under the graph is equal to the displacement of the object. You may need to use a graph to calculate the distance travelled either by shapes (splitting the area into squares and triangles) or counting squares of the graph paper.

Inertia is the tendency of a body to either stay at rest or have a constant velocity. It resists change. Inertial mass is a measure of how difficult it is to change an object’s velocity and is defined as the ratio of force over acceleration.

When accelerating, the force from the engine can be calculated using F=ma, likewise, once the deceleration is known, you can use F=ma to calculate the braking force.

The momentum of an object can be calculated using this formula:

Momentum (kgm/s) = Mass (kg) x Velocity (m/s) or p = mv

In a closed system or “an explosion” scenario, the momentum before and event is equal to the momentum after. This is crucial as momentum uses velocity to calculate it and as velocity is a vector quantity, so is momentum.