Oh Hello Welcome to my laboratory.
My name is Professor Mac, and today I’m going to be talking about Newton’s second
law of motion.
This is one of three laws which Sir Isaac Newton published in 1687.
The laws explain the interaction of forces and objects and the way in which the motion
of an object is affected by force.
The second law is an incredibly important law even although its form is rather simple.
You may have seen it before and it’s normally expressed as F=ma.
Today I’ll explain this law, and together we’ll explore the way in which we can use
it to predict how an object will change its motion when an unbalanced force acts upon
it.
So what does the F the m and the a stand for. Well F represents the force on the object.
m represents the mass of the object and a represents the acceleration of the object
resulting, from the applied force.
So using this equation it is possible for us to calculate the force acting on an object
of known mass, by observing the object’s acceleration. Alternatively, by rearranging
the equation we are able to predict the acceleration of an object of known mass, as a result of
the force acting on it. So you can see that this equation is very useful.
Now you should note that F=ma is in fact derived from the more exact definition of the second
law which is that the Force equals the rate of change of momentum of the object, where
momentum is defined as the object’s mass times its velocity.
However, today we will study the law in the form F=ma and the best way for us to do that
is to do an experiment.
Ok well here is our experimental set-up.
We have block of wood here representing our object.
And as you can see it is resting on a very smooth surface, which is so smooth we can
assume that it provides no resistance to the block moving on it.
We also have a loading device here, which we’ll use to apply a constant force to the
block as it moves along the surface.
We’ll be able to measure the force being applied to the block by observing this Newton
spring balance. This uses a spring which has been calibrated to read force in Newtons.
As the loading arm moves it exerts a force on my hand through the extension of the spring
and we get a reading of the force being applied as shown by the scale here.
So let’s do an experiment to better understand Newton’s second law of motion. Remember
that it states that Force equals mass times acceleration.
Now a very important point to note is that the force refers to the sum of the forces
on the object in a given direction. For example let’s look at the forces in the vertical
direction on this block. We have the gravity force and the force from the table onto the
block. These are in balance and therefore the net force on the block in the vertical
direction is zero.
So what does F=ma tell us about the vertical acceleration of the block when the sum of
the forces in the vertical direction is zero? Well let’s write down the equation and see.
We start with the sum of the forces in the vertical direction equals the mass of the
block times the vertical acceleration. That is F=ma with the subscript v used to indicate
that we are considering the forces and acceleration in the vertical direction. We then rearrange
the equation to give the sum of the forces in the vertical direction divided by the mass
of the block equals the vertical acceleration. So taking the sum of the vertical forces equal
to zero newtons, with N being used to represent newtons, taking the mass of the block as 5kg,
and then using the equation for acceleration, we see that this gives zero newtons,
divided by the mass of 5kg, which equals the vertical acceleration, and since zero divided
by 5 equals zero, it follows that the vertical acceleration is zero with the units meters
per second squared. We can see that this is indeed the case by observing that the block
is not moving.
So what if we introduce an unbalanced horizontal force. Well the second law tells us that if
we have an unbalanced force we will observe the object accelerating. So let’s do that
and see what happens.
Well we’re ready to perform the experiment.
As the block moves along the surface we will take a snap shot of the position of the block
at one second intervals. This will help us identify the change in motion of the block.
The block has a mass of 5kg and we will apply a force of two and a half newtons. So let’s
see what happens.
Well we have the snap-shots of the positions of the block at one second intervals. You
can see that the distance between the snap-shots increases. This means that the velocity of
the block is increasing, which means that the block is accelerating under the action
of the force.
We can check the force which was applied by looking at the recording of the Newton balance
during the test. It was attached to the block through a magnetic link between the end of
the Newton balance and a magnetic insert in the block. Once the test starts you can see
that a force of two and a half newtons was applied.
Remember that the surface here provides no resistance to the motion, so the measured
force is the only horizontal force applied to the block, and is therefore the unbalanced
horizontal force.
So what will happen if we apply a force twice as large? Let’s apply a force of 5 newtons
to the block and see what happens.
Well, looking at the snap-shots at one second intervals you can see how the block has moved
a further distance for each second under the action of the larger 5 newtons force. This is a result
of the larger force increasing the acceleration of the block.
If we have a look at the recording of the Newton balance during the test we see that
a force of five newtons was indeed applied to the block.
So now that we understand the way in which the second law works, let’s use it to predict
the force required to accelerate a block ten times the mass of the smaller blocks.
Our challenge is to predict the force we need to apply to this large block of 50kg to achieve
the same acceleration experienced by the small 5kg block when it had a force of 5 newtons
applied. So let’s use Newton’s second law to calculate the force required.
We first have to calculate the acceleration of the small 5kg block with an unbalanced
horizontal force of 5N applied. The subscript s indicates that we are referring to the small
block for this part of the calculation.
We calculate the acceleration by writing the second law in the form Force divided by mass
equals acceleration. So taking the unbalanced force equal to 5 newtons and the mass equal
to 5kg this gives five divided by five, which equals 1 meter per second squared.
To calculate the force required to accelerate the large block at 1 meter per second squared
we use the second law in the form F=ma where the subscript L indicates that we are referring
to the large block for this part of the calculation. So taking the mass of the large block as 50kg
and the acceleration the same as the acceleration of the small block, which we calculated as
1 meter per second squared, this gives the force we need to apply to the large block,
equal to 50kg times 1 meter per second squared, which gives 50 newtons.
Now this is interesting, since you can see Newton’s second law has told us that for
a block with a mass ten times larger, we need to apply a force ten times larger to get the
same acceleration. In other words, to achieve a given level of acceleration, more force
is required to accelerate an object which has more mass.
So let’s apply a force of 50 newtons to the large block and see what happens.
I’ve lined up the centre of the large block with the centre of the small block at time
zero so that we may observe the relative motion of the blocks by observing the positions of
their centre points. So let’s run the experiment.
Well comparing the positions of the snap-shots for the large block with a force of 50 newtons
applied, and the small block with a force of 5 newtons applied, we can see that the
distance between the snap-shots at one second intervals are the same. This is because they
are accelerating at the same rate, just as we predicted.
And if we have a look at the recording of the Newton balance during the test, we see
that a force of fifty Newtons was indeed applied to the 50kg block.
So, there we are, that’s how you use Newton’s Second law to control the motion of an object.
So let’s review what we’ve learned about Newton’s Second Law of Motion.
The law is expressed as Force equals mass times acceleration. We noted that the force
is the sum of the forces on an object in a given direction. If this equals zero then
the acceleration of the object is zero. We also observed that if we have a non-zero unbalanced
force applied to the object it will accelerate. The larger the force, the greater the acceleration.
And for objects with larger mass, we need to apply a larger force to get the same acceleration
as a smaller block with a smaller force applied.
Well, thank you for very much for joining me today, and I look forward to you visiting
again. For further information why don’t you visit
my website learnwithmac.com where you’ll find a tutorial on the second law and the
latest news of what else I’m doing.
So from me, Professor Mac, until next time, all the best. Bye