# Question Video: Identifying Forces in a Pulley System Physics • 9th Grade

A man holds onto a rope that is connected to a weight, strung across two pulleys, as shown in the diagram. The mass of the weight and the mass of the man are both 90 kg. When the man does not pull on the rope, neither he nor the weight moves. The man pulls downward on the rope to try and pull himself upward. Which of the following statements best describes the result of the man pulling on the rope? [A] Neither the man nor the weight moves. [B] The man moves upward and the weight stays in the same place. [C] The man moves upward and the weight moves downward. [D] The man moves downward and the weight moves upward. [E] The weight moves upward and the man stays in the same place.

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### Video Transcript

A man holds onto a rope that is connected to a weight, strung across two pulleys, as shown in the diagram. The mass of the weight and the mass of the man are both 90 kilograms. When the man does not pull on the rope, neither he nor the weight moves. The man pulls downward on the rope to try and pull himself upward. Which of the following statements best describes the result of the man pulling on the rope? (A) Neither the man nor the weight moves. (B) The man moves upward and the weight stays in the same place. (C) The man moves upward and the weight moves downward. (D) The man moves downward and the weight moves upward. (E) The weight moves upward and the man stays in the same place.

In this question, we need to think about what happens when the man from the diagram pulls the rope downward, specifically, what effect this has on the position of the man and the weight. Let’s begin by summarizing what we’re told in the main question text so that we can then clear some space. We’re told that the man and the weight have the same mass of 90 kilograms. The important thing is not the actual value of mass but rather that both masses are the same. Let’s show this by labeling both masses as 𝑚 on the diagram. The other thing we’re told is that the man pulls downward on the rope. Let’s make a note of this and clear some space.

Now, since the man and the weight have the same mass, then when the man is still and doesn’t pull on the rope, the system is balanced. So, neither the man nor the weight moves. However, we’re asked about a situation where the man does pull downward on the rope in an attempt to move himself upward. This is an interaction between a pair of objects, the man and the rope. This means we know that Newton’s third law of motion applies.

Let’s recall that this law states that a pair of interacting objects exert equal and opposite forces on each other. The man applies a downward force on the rope. By Newton’s third law, the rope then must apply an upward force on the man. So, when the man pulls, he applies a force to move his body upward with respect to the rope, which is equivalent to moving the rope he’s holding downward with respect to his body.

Since the rope is able to move freely in response to the force applied by the man, then the part of the rope that the man is holding moves downward. When this happens, the tension in the rope will cause the entire rope to move. Recall that a pulley simply changes the direction of tension in the rope so that the part of the rope that’s in between the pulleys will move to the left. And then the part of the rope that’s attached to the weight will move upward. Since the weight is attached to the rope, this net upward force of tension on the weight will cause the weight to move upward as well.

Just knowing this, we can eliminate a few answer options. Because we know that the weight must move upward, we can eliminate options (A), (B), and (C), since (A) and (B) claim that the weight doesn’t move, while (C) says that the weight moves downward, not upward.

This leaves us with only two choices. The difference between them is that answer option (D) says that the man moves downward, while option (E) says that the man stays in the same place. We can see though that there’s no reason that the man would move downward. The rope he’s holding moves downward. But remember that at the same time, the man moves upward with respect to the rope, since he’s trying to pull his body up. This results in the man experiencing no net motion, meaning his center of mass doesn’t move. All that’s happened is that he’s pulled the rope down by some amount, and the rope has pulled him up by the same amount due to Newton’s third law.

Therefore, we know that the correct answer is option (E). The weight moves upward and the man stays in the same place.