Video Transcript
The net force on an object is zero. Which of the following statements about the object must be false? (A) The speed of the object is zero. (B) The speed of the object is constant. (C) A single force with a magnitude greater than zero acts on the object. (D) Multiple forces with magnitudes greater than zero act on the object. (E) None of these statements must be false.
Okay, so this question is asking us about an object that has a net force acting on it of zero. 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, which we might also see written as the resultant force, is the vector sum of all of the individual forces that act on that object. That is, this net or resultant force is the sum of all individual force vectors.
Let’s suppose we have an object represented by this pink circle here. Let’s also 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 could say then that the net force on this object to the right is equal to 𝐹 two minus 𝐹 one.
If instead though the magnitude of the leftward force is also 𝐹 two, the same as that of the rightward force, then in this case the net force on the object to the right is equal to 𝐹 two minus 𝐹 two. We can see then that whatever the value of the magnitude 𝐹 two, the net force on the object to the right will be equal to zero. In fact, since these leftward and rightward forces are the only two forces acting on the object and we’ve seen that they cancel each other out, then we can say that the overall net force on the object is equal to zero. This example situation shown here demonstrates one way in which we can have multiple forces with nonzero magnitudes acting on an object such that the net force on that object is equal to zero.
Now, we’re being asked which of these statements about an object with a net force on it of zero must be false. We can notice that answer option (D) claims that it must be false that multiple forces with magnitudes greater than zero act on the object. But we’ve just seen a situation in which multiple forces with magnitudes greater than zero act on an object such that they do produce a net force of zero. This means then that the statement given in option (D) is not a statement that must be false, and so we can eliminate answer option (D).
It’s worth briefly mentioning that this example is just one way in which we can end up with a net force of zero acting on an object. We could, for example, also have balanced vertical forces acting in the up- and downward directions in addition to these balanced horizontal ones. In fact, we could have much more complicated situations still in which there are many forces acting on the object, just so long as the net result of these forces is that they cancel each other out. Of course, the other way to get a net force of zero acting on an object is if no forces act on that object at all.
Let’s now have a look at the statement given in answer option (C). The statement claims that if the net force on an object is zero, then it must be false that a single force with a magnitude greater than zero acts on the object. Let’s again consider this object here and think about what happens if a single force with a magnitude greater than zero 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. We can see that in this case, since this force to the right is the only force acting on the object, then there’s nothing to cancel or balance it out.
More precisely, since the net force on an object is the vector sum of all the forces acting on it, and in this case we’ve just got the one force acting to the right, then the net force on the object must be equal to this single force that acts on it. So that’s a net force to the right with a magnitude of 𝐹. And we know that this magnitude is greater than zero. So the magnitude of the net force acting on the object must also be greater than zero. In other words, if like this statement in option (C) we have a single force with a magnitude greater than zero acting on an object, this must result in a nonzero net force on that object.
By the same token then, if the net force acting on an object is zero, then it cannot be true that a single force with a magnitude greater than zero acts on the object. That is, the statement in option (C) must be false if the net force on an object is zero. And so it’s looking like option (C) may well be our answer. To be sure of this though, we should also check out the remaining answer options.
Let’s have a look at answer options (A) and (B), which talk about the speed of the object. Option (A) claims it must be false that the speed of the object is zero, while option (B) claims it must be false that the speed of the object is constant. To understand these statements, it’s going to be helpful to consider Newton’s first law of motion. This law tells us that an object at rest will remain at rest and an object moving with a constant velocity will continue to travel at that velocity unless acted on by an unbalanced force. This means 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.
If the velocity of an object doesn’t change, then there’re two possibilities for the motion of that object. The first possibility is that the object is initially not moving, so it’s got an initial speed of zero. If the object’s velocity doesn’t change, then its speed can’t change either. And so the speed of the object remains equal to zero. This case is covered in the first bit of Newton’s first law of motion, which says that if there is no unbalanced force acting on it, then an object at rest will remain at rest. We’ve just seen then how a net force of zero acting on an object can lead to the object having a speed of zero.
Since the statement in option (A) claims that it must be false that the speed of the object is zero and we’ve just seen that this can in fact be true, then we can safely eliminate answer option (A).
The other case to consider is a net force of zero acting on an object that has an initial speed that’s not equal to zero. And in this case, since we know that the object experiences no change in its velocity, then it must continue to travel at the same constant speed. Notice that the statement in option (B) is claiming that it must be false that the speed of the object is constant if the net force on that object is zero. But we’ve just seen how if a net force of zero acts on a moving object that object continues to move at a constant speed. So then, the statement in option (B) does not have to be false. And so we can safely eliminate this answer choice.
The only answer option that we’ve not yet considered is option (E), which says that none of these statements must be false. Now, we’ve shown that the statements given in options (A), (B), and (D) do not have to be false. However, we’ve also got the statement given in option (C), which we’ve shown does have to be false for an object with a net force of zero acting on it. That means we can eliminate answer option (E) and choose option (C) as our answer. If the net force on an object is zero, then it must be false that a single force with a magnitude greater than zero acts on the object.
