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In the mechanism shown in Figure (II.5), the crank AB is 75 mm long and rotates clockwise at 8 rad/s. L(BC) =300 mm and L(BD) =L(CD) =L (DE). Find the velocity and acceleration of pistons C and E. [ 615 mm /s, 210 mm/s, 4.05 m/s 2 , 9.8 m /s 2 ]?
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In the mechanism shown in Figure (II.5), the crank AB is 75 mm long an...
Solution:
Given data:
Length of crank, AB = 75 mm
Rotation speed of crank, ω = 8 rad/s
Length of BC, L(BC) = 300 mm
Length of BD = Length of CD = Length of DE = L
Velocity of piston C:
The velocity of piston C can be found by using the slider-crank mechanism equation:
vC = vB + ωAB × BC
vB = 0, as the frame is fixed
vC = ωAB × BC = 8 × 0.3 = 2.4 m/s = 2400 mm/s
Therefore, the velocity of piston C is 2400 mm/s or 2.4 m/s.
Acceleration of piston C:
The acceleration of piston C can be found by using the slider-crank mechanism equation:
aC = aB + αAB × BC + ωAB2 × BC
αAB = 0, as the crank AB rotates at a constant speed
aB = 0, as the frame is fixed
aC = ωAB2 × BC = 8^2 × 0.3 = 19.2 m/s2 = 19200 mm/s2
Therefore, the acceleration of piston C is 19200 mm/s2 or 19.2 m/s2.
Velocity of piston E:
The velocity of piston E can be found by using the slider-crank mechanism equation:
vE = vD + ωDE × DE
vD = vB + ωBD × BD
vB = 0, as the frame is fixed
ωBD = ωAB, as BD and AB are connected
vD = ωAB × BD = 8 × L
vE = ωDE × DE = ωAB × DE
In ΔBDE, using the Pythagorean theorem:
BD2 + DE2 = BE2
L2 + DE2 = (2L)2
DE = √3L
vE = ωAB × DE = 8 × √3L
vE = 8 × √3 × L = 13.856 m/s = 13856 mm/s
Therefore, the velocity of piston E is 13856 mm/s or 13.856 m/s.
Acceleration of piston E:
The acceleration of piston E can be found by using the slider-crank mechanism equation:
aE = aD + αDE × DE + ωDE2 × DE
αDE = 0, as the crank DE rotates at a constant speed
aD = aB + αBD × BD + ωBD2 × BD
αBD = αAB, as BD and AB are connected
aD = ωAB2 × BD = 8^2 × L
aE = ωDE2 × DE = ωAB2 × DE
aE = ωAB2 × DE
In ΔBDE, using the Pythagorean theorem:
BD2 + DE2 = BE2
L2 + DE2 = (2L)2
DE = √3L
aE = ωAB2 × DE = 64 × √3L
aE = 110.848 m/s
Given data:
Length of crank, AB = 75 mm
Rotation speed of crank, ω = 8 rad/s
Length of BC, L(BC) = 300 mm
Length of BD = Length of CD = Length of DE = L
Velocity of piston C:
The velocity of piston C can be found by using the slider-crank mechanism equation:
vC = vB + ωAB × BC
vB = 0, as the frame is fixed
vC = ωAB × BC = 8 × 0.3 = 2.4 m/s = 2400 mm/s
Therefore, the velocity of piston C is 2400 mm/s or 2.4 m/s.
Acceleration of piston C:
The acceleration of piston C can be found by using the slider-crank mechanism equation:
aC = aB + αAB × BC + ωAB2 × BC
αAB = 0, as the crank AB rotates at a constant speed
aB = 0, as the frame is fixed
aC = ωAB2 × BC = 8^2 × 0.3 = 19.2 m/s2 = 19200 mm/s2
Therefore, the acceleration of piston C is 19200 mm/s2 or 19.2 m/s2.
Velocity of piston E:
The velocity of piston E can be found by using the slider-crank mechanism equation:
vE = vD + ωDE × DE
vD = vB + ωBD × BD
vB = 0, as the frame is fixed
ωBD = ωAB, as BD and AB are connected
vD = ωAB × BD = 8 × L
vE = ωDE × DE = ωAB × DE
In ΔBDE, using the Pythagorean theorem:
BD2 + DE2 = BE2
L2 + DE2 = (2L)2
DE = √3L
vE = ωAB × DE = 8 × √3L
vE = 8 × √3 × L = 13.856 m/s = 13856 mm/s
Therefore, the velocity of piston E is 13856 mm/s or 13.856 m/s.
Acceleration of piston E:
The acceleration of piston E can be found by using the slider-crank mechanism equation:
aE = aD + αDE × DE + ωDE2 × DE
αDE = 0, as the crank DE rotates at a constant speed
aD = aB + αBD × BD + ωBD2 × BD
αBD = αAB, as BD and AB are connected
aD = ωAB2 × BD = 8^2 × L
aE = ωDE2 × DE = ωAB2 × DE
aE = ωAB2 × DE
In ΔBDE, using the Pythagorean theorem:
BD2 + DE2 = BE2
L2 + DE2 = (2L)2
DE = √3L
aE = ωAB2 × DE = 64 × √3L
aE = 110.848 m/s
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In the mechanism shown in Figure (II.5), the crank AB is 75 mm long and rotates clockwise at 8 rad/s. L(BC) =300 mm and L(BD) =L(CD) =L (DE). Find the velocity and acceleration of pistons C and E. [ 615 mm /s, 210 mm/s, 4.05 m/s 2 , 9.8 m /s 2 ]?
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In the mechanism shown in Figure (II.5), the crank AB is 75 mm long and rotates clockwise at 8 rad/s. L(BC) =300 mm and L(BD) =L(CD) =L (DE). Find the velocity and acceleration of pistons C and E. [ 615 mm /s, 210 mm/s, 4.05 m/s 2 , 9.8 m /s 2 ]? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about In the mechanism shown in Figure (II.5), the crank AB is 75 mm long and rotates clockwise at 8 rad/s. L(BC) =300 mm and L(BD) =L(CD) =L (DE). Find the velocity and acceleration of pistons C and E. [ 615 mm /s, 210 mm/s, 4.05 m/s 2 , 9.8 m /s 2 ]? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the mechanism shown in Figure (II.5), the crank AB is 75 mm long and rotates clockwise at 8 rad/s. L(BC) =300 mm and L(BD) =L(CD) =L (DE). Find the velocity and acceleration of pistons C and E. [ 615 mm /s, 210 mm/s, 4.05 m/s 2 , 9.8 m /s 2 ]?.
In the mechanism shown in Figure (II.5), the crank AB is 75 mm long and rotates clockwise at 8 rad/s. L(BC) =300 mm and L(BD) =L(CD) =L (DE). Find the velocity and acceleration of pistons C and E. [ 615 mm /s, 210 mm/s, 4.05 m/s 2 , 9.8 m /s 2 ]? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about In the mechanism shown in Figure (II.5), the crank AB is 75 mm long and rotates clockwise at 8 rad/s. L(BC) =300 mm and L(BD) =L(CD) =L (DE). Find the velocity and acceleration of pistons C and E. [ 615 mm /s, 210 mm/s, 4.05 m/s 2 , 9.8 m /s 2 ]? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the mechanism shown in Figure (II.5), the crank AB is 75 mm long and rotates clockwise at 8 rad/s. L(BC) =300 mm and L(BD) =L(CD) =L (DE). Find the velocity and acceleration of pistons C and E. [ 615 mm /s, 210 mm/s, 4.05 m/s 2 , 9.8 m /s 2 ]?.
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