Question

3 MOM3602 7 November 2022 QUESTION 2 Governors are used to control the mean speed of an engine, where in centrifugal governors centrifugal forces acting on rotating balls are used as a controlling mechanism. The radial inward i.e. centripetal force acting on each rotating ball of a centrifugal governor which has two rotating balls are termed a controlling force and a graph of the radius r versus the controlling force $F(r)$ is termed a controlling force curve as shown below for a Porter governor and Hartnell governor respectively. F F d b e C a r r Porter governor Hartnell governor Determine the following information: 2.1 Explain using appropriate graphs and/or equations what the necessary condition (5) $\frac{dF}{dr} > \frac{F}{r}$ for a governor to be stable actually means in physical terms and why mathematically; 2.2 Referring to the supplied graph determine and mathematically prove whether the (5) Portner governor is stable. 2.3 Referring to the supplied graph determine and mathematically prove whether the (5) Hartnell governor is stable for each of the curves ab, cd and ef respectively. Total Marks: [15]

          3
MOM3602
7 November 2022
QUESTION 2
Governors are used to control the mean speed of an engine, where in centrifugal governors
centrifugal forces acting on rotating balls are used as a controlling mechanism. The radial
inward i.e. centripetal force acting on each rotating ball of a centrifugal governor which has two
rotating balls are termed a controlling force and a graph of the radius r versus the controlling
force $F(r)$ is termed a controlling force curve as shown below for a Porter governor and Hartnell
governor respectively.
F
F
d
b
e
C
a
r
r
Porter governor
Hartnell governor
Determine the following information:
2.1 Explain using appropriate graphs and/or equations what the necessary condition (5)
$\frac{dF}{dr} > \frac{F}{r}$ for a governor to be stable actually means in physical terms and why
mathematically;
2.2 Referring to the supplied graph determine and mathematically prove whether the (5)
Portner governor is stable.
2.3 Referring to the supplied graph determine and mathematically prove whether the (5)
Hartnell governor is stable for each of the curves ab, cd and ef respectively.
Total Marks: [15]

3
MOM3602
7 November 2022
QUESTION 2
Governors are used to control the mean speed of an engine, where in centrifugal governors
centrifugal forces acting on rotating balls are used as a controlling mechanism. The radial
inward i.e. centripetal force acting on each rotating ball of a centrifugal governor which has two
rotating balls are termed a controlling force and a graph of the radius r versus the controlling
force F(r) is termed a controlling force curve as shown below for a Porter governor and Hartnell
governor respectively.
F
F
d
b
e
C
a
r
r
Porter governor
Hartnell governor
Determine the following information:
2.1 Explain using appropriate graphs and/or equations what the necessary condition (5)
(dF)/(dr) > (F)/(r) for a governor to be stable actually means in physical terms and why
mathematically;
2.2 Referring to the supplied graph determine and mathematically prove whether the (5)
Portner governor is stable.
2.3 Referring to the supplied graph determine and mathematically prove whether the (5)
Hartnell governor is stable for each of the curves ab, cd and ef respectively.
Total Marks: [15]

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