Non Calc - Potential Energy/Conserv. & Centrepital Acc?

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In summary, the first problem involves finding the tension in a vine that Jeff is swinging on, taking into account his mass and the angle of the vine. The second problem involves calculating the change in gravitational potential energy as a pendulum swings from point A to point B. Both problems can be solved by finding the change in height and using the equations for gravitational potential energy and kinetic energy. It is also noted that on a swing of any length, there will always be 3 times the force of gravity at the bottom.
  • #1
bhipps
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OMG these 2 problems are driving me insane! If you are able to help, please show steps so I can gain a good understanding...

1.) Jeff of the Jungle swings on a 7.6- vine that initially makes an angle of 32 with the vertical. If Jeff starts at rest and has a mass of 73 , what is the tension in the vine at the lowest point of the swing?

* I do know that the tension on the vine at rest is m(g) at rest...how am I supposed to incorporate theta?


2.) A 0.43 pendulum bob is attached to a string 1.2 long, making an angle of 35 with the vertical. What is the change in the gravitational potential energy of the system as the bob swings from point A to point B (from right to left)?
 
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  • #2
on the second one you could find the change in height and use. U=mgh
U= gravitational potential energy
And also on the first one you could find the change in height and use mgh and then equal this to kinetic energy to get a velocity and then use the centripetal force. This should work but I am also really tired right now.
 
  • #3
As cragar says - just calculate the change in gpe and this will tell you the KE increase, which will give you the force involved.

It's interesting to note that, on a swing of any length, if you are released with the string horizontal, you will always pull 3g at the bottom. It's just that, on a long swing, the experience lasts longer.
 

Related to Non Calc - Potential Energy/Conserv. & Centrepital Acc?

1. What is potential energy and how does it differ from kinetic energy?

Potential energy is the energy an object possesses due to its position or state. It is stored energy that can be converted into another form, such as kinetic energy. Kinetic energy, on the other hand, is the energy an object possesses due to its motion. The main difference between potential energy and kinetic energy is that potential energy is stored energy, while kinetic energy is the energy of motion.

2. What is the law of conservation of energy?

The law of conservation of energy states that energy cannot be created or destroyed, it can only be transferred or transformed from one form to another. This means that the total energy in a closed system remains constant over time.

3. How is potential energy related to conservative forces?

Conservative forces are those that do not dissipate energy and can be described by a potential energy function. This means that the work done by a conservative force is independent of the path taken, and only depends on the initial and final positions. Therefore, potential energy is directly related to conservative forces as it is a measure of the work that can be done by these forces.

4. What is centripetal acceleration and how does it relate to potential energy?

Centripetal acceleration is the acceleration an object experiences when moving in a circular path. It is always directed towards the center of the circle and its magnitude is equal to v²/r, where v is the velocity and r is the radius of the circle. Centripetal acceleration is related to potential energy in the sense that it is a result of the change in potential energy as the object moves in a circular path.

5. How is the conservation of energy used to solve problems involving potential energy and centripetal acceleration?

The conservation of energy can be used to solve problems involving potential energy and centripetal acceleration by equating the initial potential energy of the object with its final kinetic energy. This can be done by using the equation: PEinitial + KEinitial = PEfinal + KEfinal. This allows us to solve for unknown variables such as velocity, radius, or mass, by using the known values of potential and kinetic energy.

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