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Chapter 9: Q5Q (page 376)

Under what conditions does the energy equation for the point particle system differ from the energy equation for the extended system? Give two examples of such a situation. Give one example of a situation where the two equations look exactly alike.

Short Answer

Expert verified

The two examples of such a situation in whichthe energy equation for the point particle system differs from the energy equation for the extended systemare a person running uphill and a disk rotating down the incline.

The one example of a situation where the two equations look exactly alike is an object that is freely falling and not rotating.

Step by step solution

01

Significance of the types of the kinetic energy and the energy principle for the point particles

The types of kinetic energy are described as the translational and the rotational kinetic energy.

The energy principle states that energy is neither created nor destroyed, only converted from one form to another.

02

Determination of the examples of the situations

The point particles will only consist of translational kinetic energy. Therefore, the extended systems will have different energy equations if energy change occurs between them. However, the conditions for the energy for the point particle system and the extended system will differ if the extended system has elastic, chemical, internal and thermal energy. Moreover, if the extended system rotates, the equation can also be different if the point does not move with the application of normal force.

The two examples of the system are a person running uphill and a disk rotating down an inclination. In the first example, the internal energy is not considered, and in the second example, the rotational kinetic energy is not considered.

The one example of a situation where the two equations look exactly alike is an object that is freely falling and not rotating. However, if the extended system is considered in this example, only the translational kinetic energy changes, which is the only energy that changes for the system of a point particle. Hence, the two equations will be the same in this condition.

Thus, the two examples of such a situation in which the point particle system's energy equation differs from the extended system's energy equation are a person running uphill and a disk down the incline

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Most popular questions from this chapter

A man whose mass is 80kg and a woman whose mass is 50kgsit at opposite ends of a canoe 5m long, whose mass is 30kg. (a) Relative to the man, where is the mass of the system consisting of man-woman, and canoe? (Hint: Choose a specific coordinate system with a specific origin.) (b) Suppose that the man moves quickly to the center of the canoe and sits down there. How far does the canoe move in the water? Explain your work and your assumptions.

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A sphere or cylinder of mass M, radius R and moment of inertia I rolls without slipping down a hill of height h, starting from rest. As explained in problem P.33, if there is no slipping 蝇=vCM/R. (a) In terms of given variables (M,R,I and h), what is VCM at the bottom of hill? (b) If the object is a thin hollow cylinder, what is VCM at the bottom of hill? (c) If the object is a uniform density hollow cylinder, ), what isVCM at the bottom of hill? (d) If the object is a uniform density sphere what is VCM at the bottom of hill? An interesting experiment that you can perform that is to roll various objects down an inclined board and see how much time each one takes to reach the bottom.

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