What is the man's upward acceleration when hoisting himself into a tree?

In summary: Yes - but I think the problem lies in the fact that when the man pulls down on the other rope, he does so by transferring some of his "weight" to the other rope. From where else would he get any force?
  • #1
kaspis245
189
1

Homework Statement


To hoist himself into a tree, a 72 kg ties one end of a nylon rope around his waist and throws the other end over a branch of the tree. He then pulls downward on the free end of the rope with a force of 358 N . Neglect amy friction between the rope and the branch, and determine the man's upward acceleration.

Homework Equations


Newton's laws of motion.

The Attempt at a Solution


image.jpg


The answer must be a =0.14m/s2[/B]
 
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  • #2
How do you get from -2.414m/s2 (handwritten) to 0.14m/s2 (your answer)?
Suppose I changed the problem to: What force must he pull with in order to stay in place (a=0)?
 
  • #3
That's easy:
F = mg = 72 kg * 9.8 m/s2 = 705 N
 
  • #4
Firstly:
WMAN = mg = 72x9.8 = 705.6N
So force required to lift the man is 705.6N.

Surely if he pulls on the rope with a force of 358N, he won't be lifted off of the ground at all?
 
  • #5
Ben FCB Porter said:
Firstly:
WMAN = mg = 72x9.8 = 705.6N
So force required to lift the man is 705.6N.

Surely if he pulls on the rope with a force of 358N, he won't be lifted off of the ground at all?

Don't worry, I'm not this stupid, I was mimicking the other commenter hahaha!
 
  • #6
I know, but the book gives the answer that a = 0.14 m/s2 . Are you sure it's a mistake?
 
  • #7
kaspis245 said:
I know, but the book gives the answer that a = 0.14 m/s2 . Are you sure it's a mistake?

I believe that because there is a pulley, the question isn't as simple as "he weighs more than the force he exerts so therefore he must not be lifted"; have you learned about the physics of pulleys? I think that is the area of physics this question might be about...
 
  • #8
We're dealing with a fixed pulley, so it doesn't change anything.
 
  • #9
I thought the lifting force required is still reduced
 
  • #10
What about Newton's 'equal and opposite law'? When the man pulls down on the rope, does the rope not pull back up on him?
 
  • #11
Nathanael said:
What about Newton's 'equal and opposite law'? When the man pulls down on the rope, does the rope not pull back up on him?
Yes - but I think the problem lies in the fact that when the man pulls down on the other rope, he does so by transferring some of his "weight" to the other rope. From where else would he get any force?
 
  • #12
Svein said:
Yes - but I think the problem lies in the fact that when the man pulls down on the other rope, he does so by transferring some of his "weight" to the other rope. From where else would he get any force?
You can say it like that if you'd like, but that's saying exactly the same thing. The man pulls down on the rope and the rope pulls up on the man. The rope supports part of the weight of the man, and the weight of the man supported by the rope pulls down on the rope. Etc.

The reason I mention this is because the OP did not include it in his free body diagram.To the OP:
kaspis245 said:
That's easy:
F = mg = 72 kg * 9.8 m/s2 = 705 N
That's incorrect. Fix your FBD, fix your equations, and try again.

Also, in your equations you wrote, "T-F=-ma" but that "m" is not the same "m" as in the equation above it, is it?
 

1. What are Newton's three laws of motion?

Newton's first law states that an object at rest will remain at rest and an object in motion will remain in motion at a constant velocity unless acted upon by an external force. Newton's second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Newton's third law states that for every action, there is an equal and opposite reaction.

2. How do forces affect motion?

Forces can cause an object to change its speed, direction, or shape. When a force is applied to an object, it will accelerate in the direction of the force. The larger the force, the greater the acceleration. If multiple forces act on an object, their combined effect will determine the object's overall motion.

3. What is the difference between mass and weight?

Mass is a measure of the amount of matter in an object, while weight is a measure of the force of gravity acting on an object. Mass is constant, while weight can change depending on the gravitational pull of the environment. For example, an object will have the same mass on Earth and on the moon, but its weight will be different due to the difference in gravitational pull.

4. What is the relationship between force, mass, and acceleration?

According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This means that the greater the force applied to an object, the greater its acceleration will be. Similarly, the greater the mass of an object, the smaller its acceleration will be for a given force.

5. How do forces interact with each other?

Forces can interact with each other in three ways: they can be balanced, unbalanced, or equal and opposite. When forces are balanced, they cancel each other out, resulting in no net force and no change in motion. When forces are unbalanced, there is a net force that causes acceleration or deceleration. When forces are equal and opposite, they create an action-reaction pair, where one force is exerted in one direction and the other force is exerted in the opposite direction.

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