Tension Problems Given Two Weights

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In summary, when two buckets are hanging by a massless cord, the tension in each cord is determined by the gravitational force acting on the bucket and the acceleration caused by the cord.
  • #1
yandereni
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1

Homework Statement


One 3.2kg paint bucket(B) is hanging by a massless cord from another 3.2kg paint bucket(A), also hanging by a massless cord.
a.) if the buckets are at rest, what is the tension in each cord?
b.) if the two buckets are pulled upward with an acceleration of 1.6m/s2 by the upper cord, calculate the tension in each cord.

this is one of the problems I am confused with actually

Homework Equations


all i can make out is :
1. finding the tension when at rest
box[a] ==> FtensA = (agrav)(mA) + Ftens B
box ==> FtensB = (agrav)(mB)
2. finding the tension force given the acceleration 1.6m/s2
box[a]==>FtensA = mAaA +FtensB
box==>FtensB = mBaB

The Attempt at a Solution



I tried to solve for the tension when at rest and this is how it turned out:
FtensA = (9.8m/s2)(3.2kg) + FtensB
= 31.6N + 31.6N
= 63.2N
FtensB = (9.8m/s2)(3.2kg)
= 31.6N

Then I tried to solve for the tension given the acceleration
FtensA = (1.6m/s2)(3.2) + FtensB
= 5.12N + 5.12N
= 10.24N
FtensB = (1.6m/s2)(3.2kg)
= 10.24N

I really think that I'm wrong in here because its really confusing...Thanks In Advance! :)

<<Moderator note: Edited for formatting.>>
 
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  • #2
Part A you did correctly(though your calculation is a bit off). But when you take the tension of the cord given the new upward acceleration, remember that the first tension that you calculated doesn't go away. So how do you think you should approach part B with that in mind?
 
  • #3
yandereni said:
FtensA = (agrav)(mA) + Ftens B

In this case, (agrav) is the gravitational acceleration which means that mA(agrav) is the gravitational force acting on the bucket A. Since the bucket is at rest, the equation is a force balance for bucket A (all forces must sum to zero).

yandereni said:
FtensA = mAaA +FtensB
The gravitational force does not disappear just because you are accelerating the bucket. Also, since the buckets are now being accelerated, the forces should not add to zero, but perhaps one of Newton's laws can tell you what it should sum to?
 
  • #4
Oh, now it all makes sense. I forgot the part where the bucket is at rest. Thank you so much! I understand everything now. :)
 
  • #5


As a scientist, it is important to approach problems with a clear and logical thought process. In this case, the first step would be to identify the known quantities and determine what information is being asked for. From the given information, we know the masses of the two buckets (3.2kg each) and the acceleration (1.6m/s^2) when they are pulled upward.

Next, we can apply Newton's Second Law, which states that the net force on an object is equal to its mass multiplied by its acceleration (F=ma). In this case, the net force on each bucket is the tension in the cord, so we can set up equations for each bucket:

For bucket A:
FtensA = mAa
FtensA = (3.2kg)(1.6m/s^2)
FtensA = 5.12N

For bucket B:
FtensB = mBa
FtensB = (3.2kg)(1.6m/s^2)
FtensB = 5.12N

Therefore, the tension in each cord when the buckets are pulled upward with an acceleration of 1.6m/s^2 is 5.12N.

To solve for the tension when the buckets are at rest, we can apply the concept of equilibrium, where the net force on each bucket is equal to zero. In this case, the tension in each cord must be equal to the weight of the respective bucket (since there are no other forces acting on the buckets).

For bucket A:
FtensA = mAa + FtensB
0 = (3.2kg)(9.8m/s^2) + FtensB
FtensB = -31.36N

For bucket B:
FtensB = mBa
FtensB = (3.2kg)(9.8m/s^2)
FtensB = 31.36N

Therefore, the tension in each cord when the buckets are at rest is 31.36N.

It is important to note that the tension in a cord is always equal throughout the entire cord, so the tension in the upper cord is the same as the tension in the lower cord. I hope this helps clarify the problem for you. Keep practicing and don't be afraid to ask for help when needed.
 

1. How do you calculate tension in a system with two weights?

The tension in a system with two weights can be calculated by using Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the net force is the tension in the string or rope connecting the two weights. By setting up and solving equations using this law, the tension in the system can be determined.

2. What factors affect the tension in a system with two weights?

The tension in a system with two weights can be affected by several factors, including the masses of the two weights, the distance between them, and the angle of the string or rope connecting them. Additionally, any external forces acting on the weights, such as friction or air resistance, can also impact the tension in the system.

3. Can tension be negative in a system with two weights?

No, tension cannot be negative in a system with two weights. Tension is a force that acts in a specific direction, and it is always positive. If the weights are pulling in opposite directions, the tension will be positive in one direction and negative in the other, but the overall tension in the system will still be positive.

4. How do you determine the direction of tension in a system with two weights?

The direction of tension in a system with two weights can be determined by considering the direction of the forces acting on the weights. Tension acts in the opposite direction of the force pulling on the weight, so if one weight is being pulled to the right, the tension will act to the left. It is important to consider the direction of all forces in the system to accurately determine the direction of tension.

5. What is the difference between tension and weight in a system with two weights?

Tension and weight are two different forces that act in a system with two weights. Weight is the force of gravity acting on an object, while tension is a force that acts in a specific direction, often in opposition to another force. In a system with two weights, the weights will have different masses and weights, but the tension will be the same on both sides of the string or rope connecting them.

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