Motion

,par mousme5

Let’s have a critical mind !

When, sitting in the familial car, you realized you were going at 50 km/h… Not very unusual…So you decided to tell your friends you were going at 1674.4 km/h (rotational velocity of the earth) + 50 km/h when you arrived for school. Any idea of their reaction?

Any idea why a physicist will tell you your sentence was wrong ? Because you forgot to mention the frame of reference (meaning you did not mention relative to what was your motion)! Usually, speed and velocities are assumed to be relative to our starting point. It is not important to mention it in our everyday lives as we all assume we are taking the same frames of reference. However, not considering it when studying physics becomes a problem, especially later on when we will talk about relativity (HL option).

Basics of motion and illustration of a (very) simple problem involving frames of reference

We will now consider two runners, the first one going at 3km/h and the other going at 2km/h… relative to a third person sitting on a bench. We can define their motion in terms of:

Speed (m/s) : rate of change of distance.

We can know the relative motion of the first relative to the second because their speeds are given in the same frame of reference. If they were not in the same frame, they could not be compared. From the example above, you would deduce that runner one is moving away from runner two at 1 km/h.

However, speed is not a very interesting notion… and your deduction could be false. If the runners are going toward each other, our calculation is not valid! Speed does not give an indication on the direction; velocity does. Velocity is the truly important notion when talking about an object's motion.

When talking about velocity, we are considering the direction and the rate of change of displacement. We can now say that runner one is going at 3km/h east. As you may have already understood, the equivalent of distance when a direction is given is displacement.

Velocity or instantaneous velocity ?

If we take again the case of a runner, it seems obvious that in reality he does not always run at the same velocity. His velocity as it could have been measured at any instant T is called its instantaneous velocity. If we make an average of its instantaneous velocities, we have the average velocity.

Acceleration :

Taking into consideration the direction, the notion of acceleration can be introduced. Acceleration (m/s²) is defined as the rate of change of velocity.

Graphs analysis

Be careful about the labels on the axis, it would be a shame to lose easy marks because you took a displacement/time graph for a velocity time graph.

In Displacement against time graph, we can only consider two different directions (front and back) expressed by the positive and negative sign respectively. The average velocity being equal to , it is also the slope of the graph. Another way of expressing the average velocity is , where u is the initial velocity and v is the final velocity and given the velocity is changing uniformly.

As a result a straight horizontal line means the object is stationary (slope=0) and the sign of the slope gives us the sign of the velocity. From this graph it can also be inferred that

Velocity/time graphs and acceleration/time graphs can look very similar to a displacement/time graph. Once again, this is the reason why you should pay a lot of attention on the labeling of your axis. In a velocity/time graph, the sign also reflect the direction. Knowing that acceleration can be otherwise stated as the change of velocity against time, we can conclude that and so that acceleration is the slope of the line ! A straight line will mean the object is not accelerated and is either stationary or going at constant speed. The area under the graph corresponds to the distance travelled by the body.

Acceleration-time graphs are not often used in IB for calculation purposes. In fact, the slope of the line corresponds to the rate of change of acceleration (which is not a very useful notion) and the area represents the change in velocity. However, they may be given to you to test your ability to analyze or predict (Multiple-Choice Questions) the motion of an object. The object can either have no acceleration (and constant velocity), uniform acceleration (velocity increasing exponentially) and non-uniform acceleration (non-uniform velocity).

Mathematical concepts

You always have to remember that for the equations to be valid, acceleration must be constant. It should always be the case in IB. The calculations involve more advanced mathematical tools and concept such as integrals when you deal with non-uniform acceleration.

When drawing graphs, keep in mind that the acceleration function is the derivative of the velocity one which is itself the derivative of the displacement function. However, you will not use this notion in calculus for IB Physics. In fact, the equations are derived from the small equations of average velocity and displacement stated in the Graphs Analysis part.

There are two main equations you should know. At least two of them should appear in your databooklet.

One last equation can be hepfull to you to re-arranged or replace a variable in the two previous equation : .

Test your practical knowledge

Name three apparatus that could be used to measure velocities before reading the following list.

Of course, this list is non-exhaustive!

Light gates: Light gates are formed by an emitter and a receiver, a beam of li gh t is sent by the emitter to the receiver. It sends a s ignal to a data recorder when th e b ean is blocked/cut. Knowing the length of the moving obje ct and recording the time for which the light is cut, we can deduce its velocity. You can also of course use two light gates and measure the time the moving object takes to go from one gate to the next. It will be given by the time between the signal of the first gate and the signal of the second gate.

Stopwatch/Ruler: you already know these ones… However, try to be a little more imaginative in the exam.

Ticker timer: A ticker, which is a very thin metal rod (with a constant up/down or right/left motion), is making marks or dots on a strip of paper attached to the moving body. The interval of time between each dot is known and constant, making the calculation of the velocity easy. The limitation of the apparatus is for example that no heavy object can be attached to it if we want to measure its falling velocity. Other limitations: length of strip of paper, very short ranged of time are considered between each dots so if we wanted to measure a very slow change in acceleration… we might want to find another way…

Stroboscope: A stroboscope gives out flashes at a very high frequency. After adapting the frequency of the flashes given by the stroboscope to the situation studied, we can see the entire “freezed” motion of the object. A photo c o uld be taken to analyze this motion.

Fun fact : if the frequency of the flashes is more important tha n it sh ould be, you can see the object moving in the opposite direction than its actual one !

Out of the IB world: other non-IB motion measurements

Calculator Based Ranger: a device invented by calculator companies such as Texas to measure displacement, velocity and acceleration. The device measures how far you are from it and the graph of the motion can be displayed on your calculator.

Body-fixed sensors for human motion such as angular rate sensors (gyroscopes) and accelerometers.

Odometers : used in cars, they measure your speed and display it using an arrow and a circular display board.

Using lasers: if you want to know more, please read the two links below :

http://motionsystemdesign.com/mag/measuring_motion_light_1207/index1.html

http://www.sciencedaily.com/releases/1998/01/980102005652.htm

Now that you have read the course, please respond to the QCM to check your understanding !