Newton's law related question....

In summary, a man weighing 980 N sliding down a rope that can support a weight of only 755 N is possible due to the tension force of the rope being less than the weight of the man. To find the minimum acceleration without breaking the rope, Newton's second law can be applied with the weight and tension forces. The minimum speed after sliding down 8.0 m can be found by using the equation of motion for constant acceleration, v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity (which can be assumed to be 0 m/s), a is the acceleration, and s is the distance traveled.
  • #1
KneelsBoar
4
0

Homework Statement


[/B]
A man weighing 980 N slides down a rope that can support a weight of only 755 N.

a) How is this possible?
b) What is the least acceleration he can have without breaking the rope?
c) What will his minimum speed be after sliding down 8.0 m?


Homework Equations


Not specified, but I think it's ΣF = ma, and W = mg.

The Attempt at a Solution


For a) I detail here that because of the speed at which the person is moving, he weighs less than he would if he were stationary, is this correct?

For b) For this, I used "W = mg". I figured that the gravity is known and so is his weight, so I transposed this and found his mass to be 100 kg. (980/9.8). So now that I had the mass of the person, I put into the equation "W = mg", that the weight must = 755 and the mass = 100 kg and I got that -7.55 m/s2 was the speed, is this correct?

For c) I wasn't sure how to solve this question, could someone help me out?

Thank you.
 
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  • #2
KneelsBoar said:

Homework Statement


[/B]
A man weighing 980 N slides down a rope that can support a weight of only 755 N.

a) How is this possible?
b) What is the least acceleration he can have without breaking the rope?
c) What will his minimum speed be after sliding down 8.0 m?


Homework Equations


Not specified, but I think it's ΣF = ma, and W = mg.

The Attempt at a Solution


For a) I detail here that because of the speed at which the person is moving, he weighs less than he would if he were stationary, is this correct?
No.
For b) For this, I used "W = mg". I figured that the gravity is known and so is his weight, so I transposed this and found his mass to be 100 kg. (980/9.8). So now that I had the mass of the person, I put into the equation "W = mg", that the weight must = 755 and the mass = 100 kg and I got that -7.55 m/s2 was the speed, is this correct?
No.
For c) I wasn't sure how to solve this question, could someone help me out?

Thank you.
Have you drawn a free body diagram of the man, showing the forces acting on him?
 
  • #3
I attempted to draw one, but I wasn't sure how to do so or how that would help in this case.
 
  • #4
KneelsBoar said:
I attempted to draw one, but I wasn't sure how to do so or how that would help in this case.
Let's see what you drew. The first step in any mechanics problem should be to draw a free body disgram.
 
  • #5
For a) any person or body has the same weight regardless of the speed or acceleration that it has, only in speeds close to the speed of light the weight changes but this is relativity theory and I am sure the problem doesn't want us to go into relativity theory

What you trying to say in a) is that because of the acceleration (and not because of the speed) that the person has, the force of tension from the rope to the person, is less than 980N (more specifically it has to be less than 755N). We use Newton's second law on the person with the two forces acting on it, the weight W=980N and the tension T<=755N from rope. We ll have ##W-T=ma## and ##T<=755N## its just math from now on to solve for ##a>=??##.
 
  • #6
Delta² said:
For a) any person or body has the same weight regardless of the speed or acceleration that it has, only in speeds close to the speed of light the weight changes but this is relativity theory and I am sure the problem doesn't want us to go into relativity theory

What you trying to say in a) is that because of the acceleration (and not because of the speed) that the person has, the force of tension from the rope to the person, is less than 980N (more specifically it has to be less than 755N). We use Newton's second law on the person with the two forces acting on it, the weight W=980N and the tension T<=755N from rope. We ll have ##W-T=ma## and ##T<=755N## its just math from now on to solve for ##a>=??##.
@Delta2: It is contrary to Physics Forums rules and guidelines to reveal the complete solution to a problem, which is in essence what you have done here. I was hoping that the OP would be able to work all this out on his own, once he had been given some hints and been shown how to develop and properly apply a free body diagram. I think that would have be much more beneficial for his learning process than just being told how to do the problem. Please, in the future, refrain from revealing so much detailed information. Thanks.
 

Related to Newton's law related question....

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

Newton's three laws of motion are:
1. 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.
2. The force acting on an object is equal to its mass multiplied by its acceleration (F = ma).
3. For every action, there is an equal and opposite reaction.

2. How do Newton's laws apply to real-life situations?

Newton's laws apply to real-life situations in many ways. For example:
- The first law can explain why objects continue to move in a straight line unless acted upon by an external force, such as friction.
- The second law can explain the relationship between an object's mass and the force required to move it.
- The third law can explain why we feel a recoil when shooting a gun, as the force of the bullet leaving the gun is equal and opposite to the force pushing the gun back.

3. What is the difference between mass and weight in terms of Newton's laws?

In terms of Newton's laws, mass refers to the amount of matter in an object, while weight refers to the force of gravity acting on an object.
According to Newton's second law, the force required to accelerate an object (its weight) is directly proportional to its mass. This means that an object with a greater mass will require more force to accelerate it at the same rate as an object with a smaller mass.

4. Can Newton's laws be applied to non-inertial reference frames?

Yes, Newton's laws can still be applied to non-inertial reference frames, but they may require additional forces or modifications to account for the non-inertial forces acting on the object. For example, in a rotating reference frame, the centrifugal force may need to be considered in addition to the other forces acting on an object.

5. How did Newton's laws contribute to our understanding of the universe?

Newton's laws revolutionized the field of physics and our understanding of the universe. They provided a mathematical framework for explaining the motion of objects and the relationship between forces and motion. They also laid the foundation for future scientific discoveries, such as the theory of gravity and the laws of thermodynamics, which continue to shape our understanding of the universe today.

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