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# Machine Dynamics MCQ – Angular Velocity and Acceleration of the Connecting Rod

If the crank and the connecting rod are 300 mm and 1 m long respectively and the crank rotates at a constant speed of 250 r.p.m., determine the crank angle at which the maximum velocity occurs is ____

a) 45

b) 75

c) 90

d) 60

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Answer: b

Explanation: For maximum velocity of the piston : cosθ + 2cos(2θ)/2n = 0

n = l/r : 1/.3 = 3.33

therefore, θ = 75°

If the crank and the connecting rod are 600 mm and 2 m long respectively and the crank rotates at a constant speed of 250 r.p.m, determine maximum velocity of the piston in m/s is _____

a) 15

b) 17.5

c) 20

d) 10.5

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Answer: b

Explanation: maximum velocity is given by V=w.r( sinθ + sin2θ/2n)

Maximum velocity occurs at 75, n = 2/.6 = 3.33

substituting values gives Vmax = 17.5 m/s.

The crank and connecting rod of a steam engine are 0.3 m and 1.5 m in length. The crank rotates at 150 r.p.m. clockwise, determine velocity of the piston when the crank is at an angle 40 degrees from IDC.

a) 4.19

b) 5

c) 3.49

d) 3.36

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Answer: c

Explanation: We know that ratio of lengths of the connecting rod and crank, n = l/r = 1.5/0.3 = 5,

substituting the values into the formula of velocity V=w.r(sinθ + sin2 θ / 2n) gives V = 3.49 m/s.

From the data given:

Crank and connecting rod of a steam engine are 0.3 m and 1.5 m in length; The crank rotates at 150 r.p.m. clockwise.

Determine the acceleration in m/s2 of the piston for the same position(angle 40 degrees from IDC).

a) 59.27

b) 55.25

c) 65.3

d) 50.41

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Answer: a

Explanation: We know that ratio of lengths of the connecting rod and crank, n = l/r = 1.5/0.3 = 5,

substituting the values into the formula of acceleration a= ω2.r ( cosθ + cos2θ /n ) = 59.27 m/s2.

Which of the following expression represent the angular acceleration α of the connecting rod?

a) −ω2 . sin θ/n

b) −ω2 . cos θ.n

c) ω2. cos θ/n

d) ω2 . sin θ.n

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Answer: a

Explanation: Angular acceleration is the rate of change of angular velocity, for the connecting rod it depends on the length of the rod and crank’s radius. The negative signs indicate that the sense of rotation tends to reduce the angle phi.

In a slider crank mechanism, the length of the crank and connecting rod are 150 mm and 600 mm respectively. The crank position is 60° from inner dead centre. The crank shaft speed is 400 r.p.m. (clockwise). Velocity of the slider is ________

a) 6.9 m/s

b) 6.12 m/s

c) 7.32 m/s

d) 6.66 m/s

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Answer: b

Explanation: We know that ratio of the length of connecting rod and crank, n = l / r = 0.6 / 0.15 = 4, substituting the values into the formula of velocity V=w.r( sinθ + sin2 θ / 2n) gives V = 6.12 m/s.

From the data given:

The length of the crank and connecting rod are 150 mm and 600 mm

The crank position is 60° from inner dead centre. The crank shaft speed is 400 r.p.m.

Find the acceleration in m/s2 of the slider.

a) 101.5

b) 100.6

c) 98.6

d) 97.6

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Answer: c

Explanation: We know that ratio of lengths of the connecting rod and crank, n = l/r = 600/150 = 4,

substituting the values into the formula of acceleration a= ω2.r ( cosθ + cos2θ /n ) = 98.6 m/s2.

From the data given:

The length of the crank and connecting rod are 150 mm and 600 mm

The crank position is 60° from inner dead centre. The crank shaft speed is 400 r.p.m.

Find the angular acceleration in rad/s2 of the connecting rod.

a) 421

b) 400

c) 379

d)388

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Answer: c

Explanation: Angular acceleration of the connecting rod is given by (ω2.sinθ)/n hence substituting the values will give the result as 379 rad/s2.

While calculating angular acceleration of the connecting rod, sin2(θ) term is neglected.

a) True

b) False

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Answer: a

Explanation: sin2(θ) term is neglected while calculating angular acceleration of the connecting rod as it is negligible and has a very low impact in the final calculations.

In a slider crank mechanism, the length of the crank and connecting rod are 180 mm and 540 mm respectively. The crank position is 45° from inner dead centre. The crank shaft speed is 450 r.p.m. (clockwise), calculate angular velocity of the connecting rod in rad/s.

a) 10.3

b) 11.1

c) 12.2

d) 11.8

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Answer: b

Explanation: n = l/r : 540/180 = 3

angular velocity is given by ω.cos θ/n = (450*2pi / 60).cos45/3 = 11.1 rad/s.