Derive an expression for the tension in the cord

In summary, the conversation discusses a rock suspended in an elevator and immersed in water, with the elevator accelerating upwards at a magnitude of a. The tension in the cord holding the rock is derived using the equation T=mg-(ma+F), where m is the mass of the rock, g is the acceleration due to gravity, a is the acceleration of the elevator, and F is the lift of the water. This is because for an observer in the elevator, the rock is in equilibrium and the net force is zero. The acceleration of the elevator affects the buoyant force by increasing it by the amount of ma.
  • #1
lightfire
8
0
A rock with mass m = 3.10 kg is suspended from the roof of an elevator by a light cord. The rock is totally immersed in a bucket of water that sits on the floor of the elevator, but the rock doesn't touch the bottom or sides of the bucket.

Here is the part that I am stuck on:
Derive an expression for the tension in the cord when the elevator is accelerating upward with an acceleration of magnitude a .

I have concluded that
Tension=m(g-a)-1000V(g-a)

Or force of the body-force of the water displaced but it is incorrect.
 
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  • #2
For an observer in elevator, rock is in equilibrium. Net force is zero.

m(g+a)-(T+F)=0

mg-ma-T-F=0

T=mg-(ma+F)

mg: weight
ma: inertia force
T: tension
F: the lift of water
 
  • #3
lightfire said:
I have concluded that
Tension=m(g-a)-1000V(g-a)
Show how you arrived at this answer. (How does the acceleration of the elevator affect the buoyant force?)
 

1. What is the purpose of deriving an expression for the tension in the cord?

The purpose of deriving an expression for the tension in the cord is to understand the relationship between the force applied to the cord and the resulting tension in the cord. This can help in predicting and controlling the behavior of the cord in various situations.

2. How is the tension in the cord related to the force applied?

The tension in the cord is directly proportional to the force applied. This means that as the force increases, the tension in the cord also increases. This relationship is described by the equation T = F * L, where T is the tension, F is the applied force, and L is the length of the cord.

3. What factors can affect the tension in the cord?

The tension in the cord can be affected by various factors such as the magnitude and direction of the applied force, the length and material of the cord, and any external forces acting on the cord. Friction and elasticity of the cord can also impact the tension.

4. How can the tension in the cord be calculated?

The tension in the cord can be calculated by using the equation T = F * L, where T is the tension, F is the applied force, and L is the length of the cord. Alternatively, the tension can also be calculated by measuring the extension of the cord and using Hooke's law, which states that the tension is directly proportional to the extension of an elastic material.

5. Is the tension in the cord constant?

No, the tension in the cord is not constant. It can change depending on the factors mentioned above. For example, if the length of the cord is changed, the tension will also change according to the equation T = F * L. Additionally, if the cord is experiencing external forces, the tension can also change. However, in an ideal scenario with no external forces and a constant applied force, the tension in the cord will remain constant.

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