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

  • Thread starter PerpetuallyFrustrate
  • Start date
In summary, solving acceleration problems involving tension, lift force, and pulley systems requires an understanding of Newton's second law and the principles of equilibrium. By breaking down the forces acting on an object and applying the appropriate equations, one can determine the tension in ropes, the lift force exerted by pulleys, and the overall acceleration of the system. Additionally, the direction of forces must be carefully considered in order to accurately solve these types of problems. With practice and a solid grasp of the underlying concepts, solving acceleration problems involving tension, lift force, and pulley systems can become straightforward and intuitive.
  • #1
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.
 
Physics news on Phys.org
  • #2
Update

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

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

1. What is acceleration and why is it important to understand in problem-solving?

Acceleration is the rate of change of an object's velocity over time. It is important to understand because it allows us to predict how an object will move and how much force is needed to make it move. In problem-solving, knowing the acceleration helps us determine which equations and principles to use to find the solution.

2. What is tension and how does it affect acceleration in a pulley system?

Tension is the force exerted by a string, rope, or cable on an object. In a pulley system, tension is present on both sides of the pulley and is equal in magnitude. This means that the tension on one side is responsible for accelerating the object on the other side, as there is no net force acting in the opposite direction.

3. Can you explain how lift force works in relation to acceleration?

Lift force is the force that acts perpendicular to the direction of motion of an object through a fluid, such as air or water. In a pulley system, the lift force is generated by the motion of the object being lifted through the fluid. This force can affect the acceleration of the object, as it opposes the weight of the object and can either increase or decrease its acceleration depending on the direction of the lift force.

4. How can we use equations and principles to solve acceleration problems involving tension and pulley systems?

To solve acceleration problems involving tension and pulley systems, we can use Newton's second law of motion, which states that the net force on an object is equal to its mass multiplied by its acceleration. We can also use equations such as the tension equation, which relates the tension in a string to the mass and acceleration of an object, and the work-energy theorem, which relates the work done on an object to its change in kinetic energy and can be used to solve for acceleration.

5. Are there any common mistakes to avoid when solving acceleration problems involving tension and pulley systems?

One common mistake is not taking into account the direction of the forces acting on the object. It is important to properly identify and consider all forces, including tension and lift force, and their directions when using equations to solve for acceleration. Another mistake is not properly labeling or keeping track of variables, which can lead to errors in calculations. It is also important to double check units and conversions to ensure accurate solutions.

Similar threads

How Do You Calculate the Acceleration of Buckets Using Tension and Mass?
Replies
13
Views
3K
A window washer pulls herself upward using the bucket-pulley
Replies
1
Views
4K
I What is the minimum force required to lift an object?
4
Replies
128
Views
8K
Window Washer w/ Bucket-Pulley Apparatus
Replies
18
Views
4K
Monkey accelerating up and down a rope
2
Replies
38
Views
3K
I Why doesn't the released mass m2 on pulley have higher acceleration?
Replies
14
Views
1K
Understanding Tension Forces in a Slowly Rising System
Replies
1
Views
1K
Force applied on the pulley of a system
Replies
8
Views
2K
Newtonian Mechanics/Forces Question
Replies
4
Views
1K
Confusion over the reduction of force for pulleys
Replies
1
Views
3K

Hot Threads

Recent Insights

Back
Top