Video: Newton’s first law of motion

A speck of dust with a mass of 0.25 g 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 g moves at a constant speed of 25 m/s. 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?

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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.

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