### Video Transcript

The net force on an object is zero. Which of the following statements about the object must be true? (A) A single force with a magnitude greater than zero acts on the object. (B) Multiple forces with magnitudes greater than zero act on the object. (C) The speed of the object is zero. (D) The speed of the object is constant. (E) None of these statements must be true.

The question is asking us about an object that has a net force of zero acting on it. Let’s recall that force is a vector quantity, which means that it has a direction as well as a magnitude. Then, the net force on an object is the vector sum of all the individual forces that act on that object. That is, it’s equal to the sum of all the individual force vectors. Let’s suppose that we have some object that we’ve represented by this pink circle here. Let’s further suppose that there are two forces acting on this object. We’ve got a force to the left with a magnitude of 𝐹 one and a force to the right with a magnitude of 𝐹 two.

We can say then that if the magnitude 𝐹 two is larger than the magnitude 𝐹 one, the net force on this object will be directed to the right and its magnitude will be equal to 𝐹 two minus 𝐹 one. If instead though the magnitude of the rightward forces is also 𝐹 one, the same as that of the leftward force, then this net force to the right becomes equal to 𝐹 one minus 𝐹 one. And whatever the value of 𝐹 one, this will work out as zero. We can say then that in this case the net force on the object is zero.

Now, the question is asking us which of these statements that we’re given about an object must be true if the net force on that object is zero. We can notice that the statements given in options (A) and (B) are talking about the individual forces acting on the object. Option (A) claims that it must be true that a single force with a magnitude greater than zero acts on the object, while option (B) claims it must be true that multiple forces with magnitudes greater than zero act on the object. We’ve just seen a situation in which multiple forces with magnitudes greater than zero acting on an object produces a net force on that object of zero. We could say that in this case the forces acting on the object are balanced forces.

What we’ve seen here then is that it can be true that if the net force on an object is zero, the multiple forces with magnitudes greater than zero act on the object. That is, the statement given in option (B) can be true. However, there’s also another way in which we can end up with a net force on an object of zero, and that’s if there are no forces acting on the object at all. Clearly, if no forces at all act on an object, then the vector sum of all the forces acting on that object must be zero. And so, the net force on the object has to be zero. That means that the statement given in option (B) that if the net force on an object is zero, then multiple forces with magnitudes greater than zero act on the object can be true but doesn’t have to be.

Notice that we’re not asked which of these statements can be true, but rather which of them must be true. We have shown that the statement in option (B) does not have to be true. And so, we can safely eliminate this answer choice. Let’s now think about our answer option (A), which claims it must be true that a single force with a magnitude greater than zero acts on the object. Well, again, consider this object here and think about what happens if a single force acts on it. Let’s suppose that this force acts to the right and has some magnitude 𝐹 that we know is greater than zero. In this case then, the net force on the object, which is the sum of all the force vectors acting on it, must just be equal to the single force that’s acting on the object. So, that’s a net force that’s directed to the right and has a magnitude of 𝐹 that we know is greater than zero.

In other words then, if like the statement in option (A), we’ve got a single force with a magnitude greater than zero acting on an object, then this must result in a nonzero net force on the object. Then, by the same token, if the net force on an object is equal to zero, then it’s not possible for it to be true that a single force with a magnitude greater than zero acts on the object. We found then that not only does the statement in option (A) not have to be true, but in fact it must be false. This means we can safely eliminate this choice.

Let’s now turn our attention to answer options (C) and (D), which are talking about the speed of the object. Option (C) claims that if the net force on an object is zero, then it must be true that the speed of the object is zero. Meanwhile, option (D) says it must be true that the speed of the object is constant. To understand these statements, it will be helpful to recall Newton’s first law of motion. This law says that an object at rest will remain at rest and an object moving with a constant velocity will continue at that velocity, unless acted on by an unbalanced force. What this law means is that if there is no unbalanced force acting on an object, that is if the net force on the object is zero, then that object experiences no change in its velocity.

In this case, there’s then two possibilities for the motion of the object. If an object is initially at rest and its velocity doesn’t change, then that object will remain at rest. That is, if we have an object that has no net force on it and that object isn’t moving, so it’s got an initial speed of zero meters per second, then we know that at any later point in time that object still won’t be moving, and so its speed will remain constant at zero meters per second. We’ve seen then that if the net force on an object is zero, then the statement in option (C) that the speed of the object is zero can be true.

However, there’s another possibility we need to consider, and that’s the case where the object is initially moving. This case is covered by the second part of Newton’s first law, which says that if there is no unbalanced force or the net force is zero, then an object moving with a constant velocity will continue at that velocity. That means that the velocity of the object remains constant. And if an object has a constant velocity, then it’ll also has a constant speed. So, if initially an object is moving to the right with some speed 𝑉, and there’s no net force acting on that object, then at any later time that object will still be moving to the right with the same constant speed 𝑉.

We’ve seen then that the speed of the object remains constant. In fact, this statement is also true for an object at rest. In this case the speed of the object remains constant at zero meters per second. We found then that if the net force on an object is zero, then the speed of that object has to be constant. That constant speed can be zero, but it doesn’t have to be. It can also be some nonzero value. The statement given in answer option (C) then that the speed of the object is zero can be true, but it doesn’t have to be. And that means that we can eliminate answer option (C).

Option (D) though says that if the net force on an object is zero, it must be true that the speed of the object is constant. And we’ve just seen that as a result of Newton’s first law of motion, this must be the case. That is, the statement in answer option (D) must be a true statement. Lastly, since we’ve identified option (D) as a statement that must be true, we can eliminate answer option (E), which claims that none of these statements must be true.

We choose as our answer then the statement given in option (D). If the net force on object is zero, then it must be true that the speed of the object is constant.