Video: Newton’s First Law of Motion

A book at rest on a table has a weight of 8 N. At what rate is the book accelerating? What is the net force acting on the book? What magnitude force does the table apply to the book?

03:16

Video Transcript

A book at rest on a table has a weight of eight newtons. At what rate is the book accelerating? What is the net force acting on the book? What magnitude force does the table apply to the book?

Okay, so in this question, we’ve been told that we’ve got a book at rest on a table. In other words, the book is not moving. It’s just sitting there on the table. And we’ve been told that it has a weight, which will act in a downward direction on the book. And this weight is eight newtons. So now that we’ve labelled all of the information we have so far onto the diagram, let’s look at the first part of the question.

We’ve been asked to find the rate at which the book is accelerating. Now, to answer this, we can recall that acceleration is defined as the rate of change of velocity. In other words, it’s the change in velocity of an object divided by the interval of time over which that change in velocity occurs.

However, in this particular scenario, we’ve been told that the book is at rest. In other words, it’s not moving at all. And so it has a constant velocity, which we’ll call 𝑉, of zero. And hence, we can see that, actually, there is no change in velocity of the book because the velocity of the book is not changing. In other words, Δ𝑉 is zero. And if the velocity of the book is not changing over any given period of time, then the acceleration of the book is also zero. Therefore, as our answer to the first part of the question, we can say that the rate at which the book is accelerating is zero meters per second squared.

Moving on to the second part of the question then, we’ve been asked to find the net force acting on the book, in other words, the overall or resultant force acting on the book. Now, in the question, we’ve been told that the weight of the book is eight newtons. And so we might think that the net force on the book is eight newtons as well since this is the only force we’ve labeled in the diagram so far. However, we need to be a little bit careful here.

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 will remain at rest and an object moving at a constant velocity will continue to travel with that velocity unless acted on by an unbalanced force. In other words, unless an unbalanced force acts on an object, which in this situation is at rest, the object will continue to remain at rest. And this is exactly what we’ve been told is happening in this situation.

We’ve been told that the book is at rest on the table. And in order for that to be true, the forces on the object must be balanced. In other words, there must be some force exerted by the table on the book to counteract this eight-newton weight of the book. And so we can say that the table will exert an upward eight-newton force on the book in order to cancel out the downward eight-newton force. This type of force is known as the normal force. And it is called this because the force is normal to or perpendicular to or at right angles to the surface that is actually exerting the force. That’s the top of the table.

Now, this upward eight-newton force is also sometimes known as the contact force because it occurs due to the contact between the book and the table. But then, the point is that the net force on the book must be zero because, otherwise, the book would start to accelerate. And we can see that this is true because the eight-newton force upward exactly cancels out the eight-newton force downward. And so our answer to the second part of the question is that the net force acting on the book is zero newtons.

So now, we can move on to the final part of the question, “What magnitude force does the table apply to the book?” Well, luckily, we’ve just discussed this. The table applies an eight-newton upward force onto the book. And this is known as the normal force or the contact force. However, we’ve only been asked to state the magnitude of the force, in other words, the size of the force. We don’t need to worry about the direction. And so we can say that the table applies an eight-newton force onto the book.

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