Solving Acceleration Problems: Tension, Lift Force, and Pulley Systems Explained

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SUMMARY

The discussion focuses on solving acceleration problems related to tension, lift force, and pulley systems. Key calculations include determining the acceleration of a 10 kg bucket with a tension of 63 N, which results in an acceleration of 0.3 m/s². Additionally, when a person in a motionless elevator experiences a scale reading of 0.75 of their weight, the acceleration is calculated to be -0.25g, indicating downward acceleration. The lift force exerted by a 6500 kg helicopter lifting a 1200 kg car while accelerating upward at 0.6 m/s² is also analyzed, alongside the necessary force for a window washer using a pulley system.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Basic knowledge of force, mass, and acceleration (F=ma)
  • Familiarity with gravitational force calculations (Weight = mass * g)
  • Concept of tension in ropes and pulleys
NEXT STEPS
  • Learn about advanced pulley systems and their mechanical advantages
  • Study the principles of forces in non-inertial reference frames
  • Explore the dynamics of systems involving multiple masses and tensions
  • Investigate real-world applications of lift forces in aviation and engineering
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Students studying physics, educators teaching mechanics, and professionals in engineering fields who require a solid understanding of forces and motion in practical applications.

PerpetuallyFrustrate
Could someone please furnish explanations and answers to these questions?

A 10 kg bucket is lowered by a rope in which there is 63 N of tension. What is the acceleration of the bucket?

A person stands on a bathroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only .75 of the person's regular weight. Calculate the acceleration.

A 6500 kg helicopter accelerates upward at .6 meters per seconds squared while lifting a 1200 kg car. What is the lift force exerted by the air on the rotors. What is the tension in the cable (ignore its mass) that connects the car to the helicopter?

A window washer pulls herself upward using a bucket-pulley apparatus. How hard must she pull downward to raise herself slowly at constant speed? If she increases this force by 10% what will her acceleration be? The mass of the person and bucket is 65 kg.
 
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Update

I figured out the 1st and 3rd problems but I still need help on the other 2.
 
This would be better in the "Homework Help" forum.

A person stands on a bathroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only .75 of the person's regular weight. Calculate the acceleration.

Weight is force and F= ma. Normally, If you are not accelerating either up or down, your weight is the force of gravity on you and the acceleration due to gravity: g= Weight/m. If you have an additional acceleration a', then the corresponding force F= ma' is added to your weight. Here Force= mg+ ma'= Weight+ ma'= .75*Weight so ma'= .75*Weight- Weight= -.25 Weight= -.25(mg).

From ma'= -.25 mg we get a'= -.25 g. The acceleration is 1/4 the acceleration of gravity downward.

(Of course, that's just saying that 1/4 of your weight is "removed" by accelerating at (1/4)g downward.)

A window washer pulls herself upward using a bucket-pulley apparatus. How hard must she pull downward to raise herself slowly at constant speed? If she increases this force by 10% what will her acceleration be? The mass of the person and bucket is 65 kg.

At constant speed there is no acceleration up or down. The pull must exactly of set her weight and must be equal to her weight.
(Weight= mass* g= 65 kg* 9.8 m/s2 of course.)

If she pulls with "10% more force", then "excess force"- that is the force that is above that necessary to cancel her weight downward and so gives acceleration- is 0.1*weight= 0.1 m g= ma. Now solve for a.
 

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