Work-Energy Theorem: Homework Statement & Solution

In summary, the conversation discusses the concept of work done and kinetic energy in relation to a mass whirling on a frictionless table. The problem is to show that the work done in pulling a string attached to the mass equals the increase in kinetic energy as the radius of the circle changes. The person asking for guidance is unsure if they can apply the same manipulations used for the work energy theorem in cartesian coordinates and could use some guidance. It is suggested to use conservation of angular momentum, the definition of work, and integration to solve the problem.
  • #1
jgens
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Homework Statement



A mass m whirls on a frictionless table, held to circular motion by a string which passes though a hole in the table. The string is slowly pulled through the hole so that the radius of the circle changes from l1 to l2. Show that the work done in pulling the string equals the increase in kinetic energy of the mass.

Homework Equations



N/A

The Attempt at a Solution



I've already shown that the work done by a central force is path independent. Can I just apply the same manipulations used to get the work energy theorem in cartesian coordinates? I'm really not sure so I could use some guidance here.
 
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  • #2
hi jgens! :wink:

i'll guess that they want you to use conservation of angular momentum , the definition of the work done (by the tension in the string), and a bit of integration :smile:
 

FAQ: Work-Energy Theorem: Homework Statement & Solution

What is the work-energy theorem?

The work-energy theorem is a principle in physics that states the net work done on an object is equal to the change in its kinetic energy. This means that the work done by all forces acting on an object will either increase or decrease its kinetic energy, depending on the direction of the work.

How is the work-energy theorem applied?

The work-energy theorem can be applied to a variety of situations, such as calculating the work needed to accelerate an object, the work done by friction to slow down an object, or the work needed to lift an object against gravity. It is also used in many real-life applications, such as designing roller coasters or analyzing the energy consumption of machines.

What are the units of work and energy?

The SI unit for work is the joule (J), which is equivalent to a newton-meter (N∙m). The SI unit for energy is also the joule, as energy and work are directly related. In some cases, other units such as calories or foot-pounds may also be used to measure work and energy.

Can the work-energy theorem be applied to non-conservative forces?

Yes, the work-energy theorem can be applied to both conservative and non-conservative forces. However, for non-conservative forces, the work done will not only affect the object's kinetic energy but also its potential energy. In these cases, the work done by non-conservative forces is equal to the change in the object's total mechanical energy.

How is the work-energy theorem related to the law of conservation of energy?

The work-energy theorem is a specific application of the law of conservation of energy, which states that energy cannot be created or destroyed, only transferred or transformed. In the case of the work-energy theorem, the work done on an object will either increase or decrease its kinetic energy, but the total energy of the system will remain constant.

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