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

[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.

 

[PerpetuallyFrustrate]

Update

I figured out the 1st and 3rd problems but I still need help on the other 2.

 

[HallsofIvy]

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.