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.