Comprehension  check. (Part 1.)

Ex. 1. Answer the following questions.

1. How is the kinetic energy T of the particle defined?

2. What does the work-energy equation for a particle state?

3. What does the work always result in?

4. What is a major advantage of the method of work and energy?

5. Which forces does the work-energy equation involve?

6. What does the application of the work-energy method call for?

7. What diagram should be drawn for a single particle?

8. What diagram should be drawn for a system of particles?

 

Ex.2. Say whether the following statements are True or False.

1. Kinetic energy T is a vector quantity with the units of N•m  or joules (J).

2. Kinetic energy is always positive, regardless of the direction of the velocity.

3. As T is always positive, the change ∆ T must be positive as well.

4. The work-energy equation involves all the forces acting on the body and thus give rise to changes in the magnitude of the velocities.

5. The total kinetic energy is the sum of the kinetic energies of both elements of the system.

6. For a single particle an active – force diagram that shows only forces which do work should be drawn.

 

Ex. 3. Insert the verbs  in an appropriate form  into the gaps.

Equal, bring, avoid,  do, result, call, correspond, lead,  act.

1. Kinetic energy is the total work which must be done on the particle to ……it from  a state of rest to a velocity v.

2. The equation states that the total work ….. by all forces ….. on a particle during an interval of its motion from condition 1 to condition 2 ….. the corresponding change in kinetic energy of the particle.

3. The work always …..in a changeof kinetic energy.

4. When written in the form T₁ + U _1-2 = T₂ the terms ……to the natural sequence of events.

5. A major advantage of the method of work and energy is that it …...the necessity of computing the acceleration and ……directly to the velocity changes as functions of the forces which do work.

6. Application of the work-energy method …..for an isolation of the particle or system under consideration.

 

Ex.4. Use the correct form of the word in bracket.

    These two particles are joined together by a ……(connect) which is …….(friction) and ………..(capable) of any ……(form). The forces in the ……(connect) constitute a pair of equal and opposite forces, and the points of …….(apply) ofthese forces ………(necessary) have identical ………(place) components in the …….(direct) of the forces. Hence, the net work done by these internal forces is zero during any ……(move) of the system of the two ……(connect) particles. Thus, this equation  is …….(apply) to the entire system.

 

Part 2. Power.

 

The capacity of a machine is measured by the time rate at which  it can do work or deliver energy. The total work or energy output is not a measure of this capacity since a motor, no matter how small, can deliver a large amount of energy if given sufficient time. On the other hand, a large and powerful machine is required to deliver a large amount of energy in a short period of time. Thus, the capacity of a machine is rated by its power, which is defined as the time rate of doing work.

Accordingly, the power P developed by a force F which does an amountof work

U is P = dU/dt = F • d r /dt. Since d r /dt is the velocity vof the point of application of the force, we have

P = F•v                     (5)

Power is clearly a scalar quantity, and in SI units it has the units of N•m/s = J/s. The special unit for power is the watt (W),  which equals one joule per second (J/s).

 

Part 3. Efficiency.

The ratio of the work done by a machine to the work done on the machine during the same time interval is called the mechanical efficiency e_m of the machine. This definition assumes that the machine operates uniformly so that there is no accumulation or depletion of energy within it. Efficiency is always less than unity since every device operates with some loss of energy and since energy cannot be created within the machine. In mechan­ical devices that involve moving parts, there will always be some loss of energy due to the negative work of kinetic friction forces. This work is converted to heat energy which, in turn, is dissipated to the surroundings. The mechanical efficiency at any instant of time may be expressed in terms of mechanical power P by

e_{m =} P _output: P _input

In addition to energy loss by mechanical friction, there may also be electrical and thermal energy loss, in which case, the electrical efficiency e_e and thermal efficiency e_t are also involved. The overall efficiency e in such instances would be

e = e_me_ee_t