Video Transcript
The net force on an object is zero. Which of the following statements about the object must be true? (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.
Okay, so this question is about an object where the net force on it is zero, in other words, an object with no net force acting on it. We are given four potential statements about the object, and we are asked which one of those statements must be true.
In order to answer this question, we can recall that Newton’s first law of motion tells us something useful about objects with no net force on them. Specifically, that law says that an object at rest remains at rest and an object moving with a constant velocity continues to travel at that velocity unless acted on by an unbalanced force. An unbalanced force means a net force that is not zero.
So Newton’s first law of motion means that if the net force is zero, then if the object starts out at rest — so it starts out not moving at all — then the object remains at rest. And if the object starts out moving with some constant velocity, then it keeps traveling at that same velocity. In other words, the velocity of the object remains constant.
With all this in mind, let’s now look at each of the statements given to us in the question.
The first statement is that the speed of the object is zero. Now, Newton’s first law of motion tells us that for an object with no net force on it, if the object’s speed starts out at zero, then its speed will remain zero. So this statement given in option (A) could be true. However, Newton’s first law also says that the object could have a constant nonzero velocity. And the question is asking us to identify which statement must be true, not just which statement could be true. If the net force on an object is zero, then the speed of that object could be zero, but it doesn’t have to be. So the statement given in option (A) doesn’t have to be true. So this is not our answer.
If we now look at the statement in option (B), we see this says the speed of the object is constant. Newton’s first law of motion tells us that for an object with zero net force on it, if the object’s velocity is zero, it remains as zero. And if the object’s velocity is any constant nonzero value, it remains as that same constant value. In both of these two cases, the speed of the object is constant. In one case, that constant is zero. And in the other, that constant is any nonzero value. Either way, for an object with no net force on it, the statement in option (B) must be true.
The statement in option (C) says that a single force with a magnitude greater than zero acts on the object. Now, if the net force on an object is zero, this means that whatever combination of forces might be acting on that object, there is zero overall resultant force. So any forces acting must somehow cancel each other out. This means that if we have an object like this and that object has a force on it acting to the right, then it must also have a force on it acting to the left so that these two forces cancel each other out.
An object that has a single force with a magnitude greater than zero acting on it cannot possibly have a net force on it of zero because there’s nothing to cancel this force out. So the statement given in option (C) cannot be true.
Lastly, we’ll consider the statement given in option (D). That is, multiple forces with magnitudes greater than zero act on the object. Now, this statement certainly can be true. For example, we saw how we could have an object that has one force acting to the right and another force acting to the left. If those two forces have exactly the same magnitudes as each other, then they’ll cancel each other out so that the net force on the object is zero.
However, this statement in option (D) doesn’t have to be true. One way to get a net force of zero is to have multiple forces that cancel each other out. But we could also get a net force of zero by having no forces acting at all. So the statement that multiple forces must act on the object isn’t necessarily true. This means that our answer to this first part of the question is that the statement about the object that must be true is the one given in option (B) that the speed of the object is constant.
Let’s now look at the second part of the question.
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.
So we’re given the same four potential answers as in the first part of the question. But this time, we are asked to work out which statement has to be false. We’ve pretty much already done the work needed to answer this question.
We worked out that for an object with a net force on it of zero, Newton’s first law means that the object’s speed must remain constant. This means that the statement in option (B) must be true. It also means that the statement given in option (A) could be true because that constant speed of the object could be a constant speed of zero. We also saw that if the net force on an object is zero, this means that either there are no forces acting on that object at all or there are multiple forces acting but those forces are balanced so that they cancel each other out.
The statement in option (C) is that there is a single force acting on the object. A single force must be unbalanced, and the net force cannot be zero. So this statement cannot be true. Meanwhile, the statement in option (D) is that multiple forces with magnitudes greater than zero act on the object. Now, this could be the case because if we have multiple forces, those forces could be balanced such that the net force is zero. So the statement in option (D) could be true.
Overall, the only statement here that cannot possibly be true is the one given in option (C). So our answer to this second part of the question is that if the net force on an object is zero, then the statement about that object that must be false is the one given in option (C) that a single force with a magnitude greater than zero acts on the object.
