Video Transcript
A speck of dust with a mass of 0.25
grams in deep space very far from any other objects is at rest. In another completely different
part of deep space that is also very far from any other objects, a tiny ice crystal
with a mass of 0.75 grams moves at a constant speed of 25 metres per second. What is the speck of dust’s rate of
acceleration? What net force acts on the speck of
dust? What is the ice crystal’s rate of
acceleration? What net force acts on the ice
crystal?
Okay, so, in this question we,
first of all, got a speck of dust. Let’s say this is the speck of
dust. And we’ve been told that it has a
mass of 0.25 grams. And the speck of dust is in deep
space very far from any other objects, which means that no other objects can exert
any forces on it. And because the speck of dust is in
deep space specifically away from any other objects, this means that there’s no
gravitational forces acting on the speck of dust either. Now we’ve been told that this speck
of dust is at rest. In other words, the velocity of the
speck of dust, which we’ll call 𝑣, is equal to zero metres per second.
Now as well as this, we’ve been
told that in another completely different part of deep space, also very far from any
other objects, we’ve got a tiny ice crystal. And this ice crystal has a mass of
0.75 grams. Now as well as this, we’ve been
told that this ice crystal moves at a constant speed of 25 metres per second. So, lets arbitrarily choose that
the ice crystal is moving towards the right and say that it has a velocity, which
we’ll call 𝑣, of 25 metres per second. Because that’s what we’ve been told
in the question.
Now in the first part of the
question, we’ve been asked to find the speck of dust’s rate of acceleration. In other words, what is the
acceleration of the speck of dust? Well, to answer this question, we
need to recall that acceleration, which we’ll call 𝑎, is defined as the change in
velocity of an object divided by the time interval over which that velocity change
occurs. In other words, the acceleration of
an object is equal to the rate of change of the object’s velocity.
So, if we’re trying to find the
acceleration of the speck of dust first of all, we need to realise that the speck of
dust is at rest. In other words, its velocity is
zero metres per second. And that velocity is a
constant. In other words, the velocity is not
changing. And as well as this, because the
speck of dust is away from any other object in very deep space, we know that there
are going to be no forces acting on the speck of dust.
Therefore, we can confidently say
that the change in velocity of the speck of dust is zero because the velocity is not
changing. And if the Δ𝑣 in the numerator of
the fraction on the right-hand side is zero, then this means that the acceleration
of the speck of dust must also be zero. And hence, we can say that the
speck of dust’s rate of acceleration is zero metres per second squared. At which point, we can move on to
the second part of the question.
What net force acts on the speck of
dust? Well, to answer this question, we
need to recall Newton’s first law of motion. Newton’s first law of motion tells
us that an object at rest remains at rest and an object moving with a constant
velocity continues to travel with that velocity, unless acted on by an unbalanced
force.
Now in this situation, we’ve been
told that this speck of dust is at rest. And because it’s far away from any
other object, once again, this means that it has no forces acting on it. Therefore, there is no chance of an
unbalanced force acting on the speck of dust because there are no forces acting on
the speck of dust in the first place. But then, if there are no
unbalanced forces acting on the speck of dust, then this means that the net force on
the speck of dust is zero.
And so, we can say that the net
force on the speck of dust is zero newtons. And once again, this is because the
speck of dust will remain at rest. And therefore, it is impossible for
the speck of dust to have any unbalanced forces on it. So, our suspicions that the fact
that the speck of dust is far away from any other object in space, meaning that
there are no forces acting on the speck of dust, has proven true.
So, with all of that being said,
let’s look at the next part of the question. What is the ice crystal’s rate of
acceleration? So, now we’re focusing on this ice
crystal here. We’ve been told that the ice
crystal is moving with a constant velocity of 25 metres per second. And once again, we can see that
acceleration is defined as the rate of change of velocity. In other words, the change in
velocity of an object divided by the time taken for that change in velocity to
occur.
But then, for the ice crystal, it’s
moving at a constant speed. In other words, the velocity of the
ice crystal is always 25 metres per second. And therefore, there is no change
in velocity at all, or Δ𝑣 is equal to zero. And so, just like the speck of
dust, we can say that the ice crystal’s rate of acceleration is zero metres per
second squared.
Now this might seem strange at
first. We’ve been told that the speck of
dust is stationary but the ice crystal is moving. However, the key thing about
acceleration is a change in velocity. And in both these cases, the
velocities of these objects are not changing. Therefore, they’re both
experiencing an acceleration of zero metres per second squared. So, now let’s look at the final
part of the question. What net force acts on the ice
crystal?
Now once again, looking at Newton’s
first law of motion, we can see that an unbalanced force acting on an object would
result in a change in velocity of the object. Because the first law is telling us
that an object at rest remains at rest, unless there’s an unbalanced force acting on
it. And similarly, an object travelling
at a constant velocity continues to move with that constant velocity, unless there’s
an unbalanced force on it.
Well, in this case, we’ve got an
ice crystal moving at a constant velocity. And so, there cannot be an
unbalanced force acting on it. And yet again, the ice crystal is
also in deep space far away from any other objects. So, we expect it to have no forces
acting on it. Therefore, there can be no
unbalanced forces acting on the crystal. But more importantly, the net, or
overall, force on the crystal is zero newtons.
And so, what we see from this
question is that we can have objects that are completely stationary or we can have
objects that are moving at a constant velocity. And yet, because they both have an
acceleration of zero, they both, therefore, have a net force of zero newtons acting
on them.
