Applying Newton's laws

In summary, the problem involves an 8 kg monkey climbing up a massless rope over a frictionless tree limb and down to a 15 kg package. The question is asking for the monkey's minimum acceleration to lift the crate. With a weight of 78.4N, the monkey needs an acceleration of 8.575 m/s^2 to lift the crate. However, if the monkey stops climbing and only holds onto the rope, the net force becomes 68.6N and the acceleration is 2.98 m/s^2. This may be incorrect and further guidance is needed.
  • #1
mbisCool
136
0

Homework Statement



A 8 kg monkey climbs up a massless rope that runs over a frictionless tree limb and back down to a 15 kg package on the ground.

Assume that after the package has been lifted, the monkey stops its climb and holds onto the rope.
(b) What is the monkey's acceleration?

Homework Equations



F=ma

The Attempt at a Solution



The first question was to find the minimum acceleration the monkey must have to lift the crate. I got a=8.575 m/s^2.

If the monkey stops climbing I believe it no longer has the acceleration of 8.575 so the only forces acting on it are gravity and the rope. Because the monkey is 8kg and the crate is 15kg i believe the crate would then begin to fall simultaneously raising the monkey due to its weight being greater than the monkey's. The weight of the monkey is 78.4N. subtract that from the weight of the crate gives 147N-78.4N and i get 68.6N which should be the net force. I then divided the net force by the mass of system of 23kg to get a=2.98.

Im pretty sure this is incorrect. Any hints in the right direction or indication of my error(s) would be greatly appreciated as always :)
 
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  • #2
Yet again my issue was with the website not my work :/

I got it
 
  • #3




Your attempt at finding the acceleration is on the right track, but it is missing a crucial factor - the tension in the rope. The monkey's acceleration is determined by the net force acting on it, which in this case is the difference between the weight of the monkey and the tension in the rope. So the correct equation would be:

Fnet = ma = T - mg

Where T is the tension in the rope, m is the mass of the monkey, and g is the acceleration due to gravity. Since the monkey is not climbing and the crate is not moving, the net force must be zero. This means that T = mg, and we can substitute this into the equation above to get:

Fnet = ma = mg - mg = 0

Therefore, the monkey's acceleration is zero, as expected when it is holding onto the rope and not moving. It is important to always consider all the forces acting on an object when using Newton's laws, and in this case, the tension in the rope is a crucial component. Keep up the good work!
 

What are Newton's three laws of motion?

Newton's three laws of motion are: 1) an object will remain at rest or in a state of uniform motion unless acted upon by an external force, 2) force equals mass times acceleration, and 3) for every action, there is an equal and opposite reaction.

How do Newton's laws apply to everyday situations?

Newton's laws can be applied to everyday situations such as driving a car, throwing a ball, or riding a bike. For example, when driving a car, the first law explains why the car stays in motion unless acted upon by the brakes, the second law explains how much force is needed to accelerate the car, and the third law explains why the car moves forward when the wheels push against the ground.

Can Newton's laws be broken or disproved?

No, Newton's laws have been extensively tested and have been found to accurately describe the motion of objects in most situations. However, they do not apply to extreme conditions such as at the atomic or subatomic level, or in cases of very high speeds or strong gravitational forces.

How does Newton's laws relate to other branches of science?

Newton's laws are the foundation of classical mechanics and are used in many other branches of science, such as engineering, astronomy, and biology. They also form the basis for many other laws and theories, such as the law of universal gravitation and the theory of relativity.

How can Newton's laws be used to solve problems?

Newton's laws can be used to solve problems by breaking down a complex situation into individual forces and applying the laws to each force. This allows for the calculation of unknown quantities such as acceleration, force, or mass. Using these laws, scientists and engineers can predict and manipulate the motion of objects to solve real-world problems.

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