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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

You hold up an object that consists of two blocks at rest, each of massM=5kg, connected by a low-mass spring. Then you suddenly start applying a larger upward force of constant magnitudeF=167N(which is greater than2Mg). Figure9.60shows the situation some time later, when the blocks have moved upward, and the spring stretch has increased.

The heights of the centers of the two blocks are as follows:

Initial and final positions of block 1:y1i=0.3m,y1f=0.5m

Initial and final positions of block 2:y2i=0.7m,y2f=1.2m

It helps to show these heights on a diagram. Note that the initial center of mass of the two blocks isy1i+y1i/2, and the final center of mass of the two blocks isrole="math" localid="1656911769231" y1f+y1f/2. (a) Consider the point particle system corresponding to the two blocks and the spring. Calculate the increase in the total translational kinetic energy of the two blocks. It is important to draw a diagram showing all of the forces that are acting, and through what distance each force acts. (b) Consider the extended system corresponding to the two blocks and the spring. Calculate the increase of(Kvib+Us), the vibrational kinetic energy of the two blocks (their kinetic energy relative to the center of mass) plus the potential energy of the spring. It is important to draw a diagram showing all of the forces that are acting, and through what distance each force acts.

Two people with different masses but equal speeds slide toward each other with little friction on ice with their arms extended straight out to the slide (so each has the shape of a “I”). Her right hand meets his right hand, they hold hands and spin 90°, then release their holds and slide away. Make a rough sketch of the path of the center of mass of the system consisting of the two people, and explain briefly. (It helps to mark equal time intervals along the paths of the two people and of their center of mass.)

Discuss qualitatively the motion of the atoms in a block of steel that falls onto another steel block. Why and how do large-scale vibrations damp out?

A thin uniform-density rod whose mass is 1.2kg and whose length is 0.7mrotates around an axis perpendicular to the rod, with angular speed 50radians/s. Its center moves with a speed of 8m/s.

(a) What is its rotational kinetic energy?

(b) What is its total kinetic energy?

Consider a system consisting of three particles:

m1=2kg,v→1=(8,-6,15)m/sm2=6kg,v→2=(-12,9,-6)m/sm3=4kg,v→3=(-24,34,23)m/s

What isKrel, the kinetic energy of this system relative to the centre of mass?
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