Forces and Acceleration
Introduction
In this title we are going to explore how forces change a body’s acceleration. We will examine how forward forces and backward forces acting on a body can be added together.
We are going to do this by looking at a scenario of a car under the force of its engine (forward force) and both brakes and air resistance (backward forces).
Finally, we will look at GCSE exam questions where we can apply what we have learned.
Background
Galileo was the first person to realise that a moving body will just carry on moving with a constant speed if no forces act on it.
A body will move in a straight line at constant speed unless a force acts on it
An ice skater moves very much as though no forces are slowing him down, here the friction is very low.
Most things that we see in the world at rest i.e. motionless, are due to a force caused by friction which we will investigate soon.
Click on the plus sign to apply a forward force to the car.
Keep clicking until you have a sizeable force of more than 100 Newtons (that’s what the N stands for, it is the units we measure force with).
Notice that the car gathers speed (accelerates).
Wait for the car to be moving at around 20 m/s (that’s how many metres per second it is going at). Then:
• Reduce the Forward force to zero;
• Note the speed of the car;
• Switch off the Air Resistance.
Notice that the car now moves at a constant speed as there are no forces acting on it. You brought the forward force back down to zero and you switched off the air resistance. This is Newton’s First Law in action!
By doing this simple scenario, you have already seen the consequence of applying a forward force. The object moves in the direction of the force being applied. The motion is acceleration which is the increase in speed.
Acceleration is measured by how much speed is gained every second. So, a speed might be 5 m/s and go up to 7 m/s in one second. This is an acceleration of 2 m/s per second.
You have seen acceleration in the e-scenario by noticing the increase in speed.
In the e-scenario switch off the air resistance and apply a forward force of about 10 N.
Using a stopwatch or a clock with a second hand note the speed, wait ten seconds, and note the speed again, there’s no need to be accurate.
Subtract the smaller speed from the larger one and divide by 10. This is the acceleration, it is the gain in speed (i.e. the final speed minus the initial speed) per second (you did 10 seconds, so you divided by 10).
Acceleration = change in speed/ time
Mathematically we might write:
A = (v2 – v1)/t
How Force Changes Acceleration
Run the scenario:
•Turn off air resistance.
•Change the Mass of the car to something small like 10kg.
•Apply a force of 10N.
•Note the gain in speed over 10 seconds.
•Calculate the acceleration as you did above.
Do this again (you can stop the car by pressing on Apply Brake), but this time make the mass 20 kg.
Your result for the second acceleration with 20kg should be half that for the one with 10kg.
You have just discovered Newton’s Second Law.
Newton’s Second Law
Force = Mass x Acceleration
This tells us that a body accelerates at a rate proportional to the size of the force and inversely to its mass. The mass of the object impedes acceleration.
For our car of 10kg and given a forward force of 10N the acceleration (Acceleration = Force/Mass) = 10N/10kg = 1 m/s^2
Braking Resistance
All cars have brakes, and this one is no different.
Take the car up to a good speed and try applying the brake. This adds a force as given here, 5000N, backwards to slow the car, it also cancels the forward force (like taking your foot of the accelerator and applying the brake. See how quickly is comes to a halt.
Try braking with different braking forces.
Air Resistance
The air resistance of cars depends on a few factors, for example:
•The frontal area of the car;
•The speed of the car;
•The aerodynamics of the car.
The main factor is the speed, the air resistance is proportional to the speed squared, so it is rather insignificant at low speeds, but becomes increasingly significant at higher speeds.
Run the e-scenario and with the air resistance on and the Mass at 500kg, give a forward force of 100N.
Notice how the air resistance slowly builds, slowing down the acceleration.
When the resistance is just slightly less than the forward force, the acceleration is close to zero.
Eventually the air resistance will match the forward force, and the car will have reached terminal velocity, i.e. it will cease accelerating.
Try this for different forward forces and note the terminal velocities.
You may also note that there is no terminal velocity if there is only a forward force, the car will accelerate for ever.
Note that In the scenario the car’s forward force is set to zero when it reaches 45m/s.
Stopping distances
Using the ‘Apply Brake’ button when the car is in motion shows you how having more braking power slows the car quicker meaning that the car comes to a halt quicker.
Unfortunately, that is not the whole story. There is also a small thinking time to add. From the point the driver notices an obstacle, to the time they get their foot on the brake pedal takes an appreciable time.
There will be no braking during this thinking time and if the thinking time is 0.5s and the car is travelling at 30 m/s then the distance travelled in this thinking time will be:
0.5s * 30 m/s = 15m
Which is far from insignificant.
You can test your reaction time online, for example Human Benchmark - Reaction Time Test.
Use this, or a similar site, to find out what your thinking distances would be at 30m/s and 50m/s.
Clearly when calculating stopping distances, this needs to be added to the total.
Exam Questions
AQA May 25 Foundation Paper 1
If you have difficulty answering this, try the e-scenario alongside the section above on Air Resistance.
Here we have Newton’s second law.
Just plug the given values into the equation.
If you have difficulty answering this, try the e-scenario alongside the section above on Air Resistance.
If you have difficulty answering this, try the e-scenario alongside the section above on Stopping Distances.
Read off the thinking distance for 100km/h by going to the 100 mark on the horizontal axis and then straight up to the solid line. Read the distance from the vertical axis at this point.
Read off the braking distance for 100km/h by going to the 100 mark on the horizontal axis and then straight up to the dotted line. Read the distance from the vertical axis at this point.
Add the two together to get the total stopping distance.
Make sure to take note of the word ‘increase’. It’s very easy to assume you are being asked what makes the stopping distance shorter!
Obviously new brakes and new tyres will improve stopping distance, as will driving up hill.
Don’t be confused by the use of the term ‘velocity’, in this case it is really just speed.
If you have problems, repeat how you found your acceleration using the e-scenario and the section on How Force Changes Acceleration.
In this case the change in velocity and time can be found from the graph