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# Machine Dynamics MCQ – Fluctuation of Energy

The maximum fluctuation of speed is the

a) difference of minimum fluctuation of speed and the mean speed

b) difference of the maximum and minimum speeds

c) sum of the maximum and minimum speeds

d) variations of speed above and below the mean resisting torque line

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Answer: b

Explanation: The difference between the maximum and minimum speeds during a cycle is called the maximum fluctuation of speed. The ratio of the maximum fluctuation of speed to the mean speed is called coefficient of fluctuation of speed.

The coefficient of fluctuation of speed is the _____________ of maximum fluctuation of speed and the mean speed.

a) product

b) ratio

c) sum

d) difference

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Answer: b

Explanation: The difference between the maximum and minimum speeds during a cycle is called the maximum fluctuation of speed. The ratio of the maximum fluctuation of speed to the mean speed is called coefficient of fluctuation of speed.

In a turning moment diagram, the variations of energy above and below the mean resisting torque line is called

a) fluctuation of energy

b) maximum fluctuation of energy

c) coefficient of fluctuation of energy

d) none of the mentioned

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Answer: a

Explanation: The fluctuation of energy may be determined by the turning moment diagram for one complete cycle of operation.The variations of energy above and below the mean resisting torque line are called fluctuation of energy.

If E = Mean kinetic energy of the flywheel, CS = Coefficient of fluctuation of speed and Δ E = Maximum fluctuation of energy, then

a) ΔE = E / CS

b) ΔE = E2 × CS

c) ΔE = E × CS

d) ΔE = 2 E × CS

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Answer: d

Explanation: ΔE = Maximum K.E. — Minimum K.E. = 2 E × CS

The ratio of the maximum fluctuation of energy to the ___________ is called coefficient of fluctuation of energy.

a) minimum fluctuation of energy

b) workdone per cycle

c) coefficient of fluctuation of energy

d) none of the mentioned

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Answer: b

Explanation: Coefficient of fluctuation of energy is defined as the ratio of the maximum fluctuation of energy to the work done per cycle. It is usually denoted by CE.

Due to the centrifugal force acting on the rim, the flywheel arms will be subjected to

a) tensile stress

b) compressive stress

c) shear stress

d) none of the mentioned

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Answer: a

Explanation: The following types of stresses are induced in the rim of a flywheel:

1. Tensile stress due to centrifugal force,

2. Tensile bending stress caused by the restraint of the arms, and

3. The shrinkage stresses due to unequal rate of cooling of casting. These stresses may be very high but there is no easy method of determining. This stress is taken care of by a factor of safety.

The tensile stress in the flywheel rim due to the centrifugal force acting on the rim is given by

a) ρ v2/4

b) ρ v2/2

c) 3ρ v2/4

d) ρ v2

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Answer: d

Explanation: Tensile stress in the flywheel rim due to the centrifugal force = ρ v2

where ρ = Density of the flywheel material, and

v = Linear velocity of the flywheel.

The cross-section of the flywheel arms is usually

a) elliptical

b) rectangular

c) I-section

d) L-section

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Answer: a

Explanation: The cross-section of the arms is usually elliptical with major axis as twice the minor axis, and it is designed for the maximum bending stress.

In order to find the maximum bending moment on the arms, it is assumed as a

a) simply supported beam carrying a uniformly distributed load over the arm

b) fixed at both ends (i.e. at the hub and at the free end of the rim) and carrying a uniformly distributed load over the arm.

c) cantilever beam fixed at the hub and carrying a concentrated load at the free end of the rim

d) none of the mentioned

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Answer: c

Explanation: Due to the torque transmitted from the rim to the shaft or from the shaft to the rim, the arms will be subjected to bending, because they are required to carry the full torque load. In order to find out the maximum bending moment on the arms, it may be assumed as a centilever beam fixed at the hub and carrying a concentrated load at the free end of the rim.

The diameter of the hub of the flywheel is usually taken

a) equal to the diameter of the shaft

b) twice the diameter of the shaft

c) three times the diameter of the shaft

d) four times the diameter of the shaft

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Answer: b

Explanation: The diameter of hub is usually taken as twice the diameter of shaft and length from 2 to 2.5 times the shaft diameter. It is generally taken equal to width of the rim.