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A pulley is supported midway between the two bearings spaced 400 mm apart on a shaft rotating at 1400 rpm. The tensions acting vertically downwards on the tight and slack side of the belt are 1000 N and 500 N respectively. The material of the shaft is 30 C8 steel with Se= 280MPa,Su = 600MPa,
kf = 1.85 FOS = 3, the diameter of the shaft
- a)28 mm
- b)25 mm
- c)32 mm
- d)35 mm
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A pulley is supported midway between the two bearings spaced 400 mm a...
Given
L = 400 mm,
N = 1400 rpm,
T1 = 1000 N,
T2 = 500 N,
S’e 280 MPa, Sut = 600 MPa
Kt = 1.85, F. S = 3
= 150000 N-m
(∵Shaft is subjected to complete reverse load σm = 0)
∴ d = 32 mm
Most Upvoted Answer
A pulley is supported midway between the two bearings spaced 400 mm a...
Given Data:
Distance between bearings = 400 mm
Rotational speed = 1400 rpm
Tension on the tight side of the belt = 1000 N
Tension on the slack side of the belt = 500 N
Material of the shaft = 30 C8 steel
Se = 280 MPa
Su = 600 MPa
kf = 1.85
FOS = 3
To find: Diameter of the shaft
Solution:
1. Calculation of Power transmitted:
Power (P) = (T1 - T2) × V
Where,
T1 = Tension on the tight side of the belt = 1000 N
T2 = Tension on the slack side of the belt = 500 N
V = Peripheral velocity of the pulley
d = Diameter of the pulley
Given,
Distance between bearings = 400 mm
Radius of the pulley = 400/2 = 200 mm
Rotational speed = 1400 rpm
Peripheral velocity (V) = πdN/60
Where,
N = Rotational speed in rpm
Substituting the values, we get:
V = π × 200 × 1400/60 = 4398.23 mm/min
Power transmitted (P) = (1000 - 500) × 4398.23/1000 = 2199.11 W
2. Calculation of Bending Moment:
Bending moment (M) = P × L/4
Where,
L = Distance between bearings = 400 mm
Substituting the values, we get:
M = 2199.11 × 400/4 = 219911 N-mm
3. Calculation of Diameter of the Shaft:
Diameter of the shaft (d) = (16M/πkf)^(1/3)
Where,
kf = Factor of safety = FOS = 3
Substituting the values, we get:
d = (16 × 219911/π × 1.85 × 3)^(1/3) = 32.21 mm
Rounding off to the nearest integer, we get the diameter of the shaft as 32 mm.
Therefore, option (c) is the correct answer.
Distance between bearings = 400 mm
Rotational speed = 1400 rpm
Tension on the tight side of the belt = 1000 N
Tension on the slack side of the belt = 500 N
Material of the shaft = 30 C8 steel
Se = 280 MPa
Su = 600 MPa
kf = 1.85
FOS = 3
To find: Diameter of the shaft
Solution:
1. Calculation of Power transmitted:
Power (P) = (T1 - T2) × V
Where,
T1 = Tension on the tight side of the belt = 1000 N
T2 = Tension on the slack side of the belt = 500 N
V = Peripheral velocity of the pulley
d = Diameter of the pulley
Given,
Distance between bearings = 400 mm
Radius of the pulley = 400/2 = 200 mm
Rotational speed = 1400 rpm
Peripheral velocity (V) = πdN/60
Where,
N = Rotational speed in rpm
Substituting the values, we get:
V = π × 200 × 1400/60 = 4398.23 mm/min
Power transmitted (P) = (1000 - 500) × 4398.23/1000 = 2199.11 W
2. Calculation of Bending Moment:
Bending moment (M) = P × L/4
Where,
L = Distance between bearings = 400 mm
Substituting the values, we get:
M = 2199.11 × 400/4 = 219911 N-mm
3. Calculation of Diameter of the Shaft:
Diameter of the shaft (d) = (16M/πkf)^(1/3)
Where,
kf = Factor of safety = FOS = 3
Substituting the values, we get:
d = (16 × 219911/π × 1.85 × 3)^(1/3) = 32.21 mm
Rounding off to the nearest integer, we get the diameter of the shaft as 32 mm.
Therefore, option (c) is the correct answer.
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A pulley is supported midway between the two bearings spaced 400 mm apart on a shaft rotating at 1400 rpm. The tensions acting vertically downwards on the tight and slack side of the belt are 1000 N and 500 N respectively. The material of the shaft is 30 C8 steel with Se= 280MPa,Su = 600MPa,kf = 1.85 FOS = 3, the diameter of the shafta) 28 mmb) 25 mmc) 32 mmd) 35 mmCorrect answer is option 'C'. Can you explain this answer?
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A pulley is supported midway between the two bearings spaced 400 mm apart on a shaft rotating at 1400 rpm. The tensions acting vertically downwards on the tight and slack side of the belt are 1000 N and 500 N respectively. The material of the shaft is 30 C8 steel with Se= 280MPa,Su = 600MPa,kf = 1.85 FOS = 3, the diameter of the shafta) 28 mmb) 25 mmc) 32 mmd) 35 mmCorrect answer is option 'C'. Can you explain this answer? 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 A pulley is supported midway between the two bearings spaced 400 mm apart on a shaft rotating at 1400 rpm. The tensions acting vertically downwards on the tight and slack side of the belt are 1000 N and 500 N respectively. The material of the shaft is 30 C8 steel with Se= 280MPa,Su = 600MPa,kf = 1.85 FOS = 3, the diameter of the shafta) 28 mmb) 25 mmc) 32 mmd) 35 mmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A pulley is supported midway between the two bearings spaced 400 mm apart on a shaft rotating at 1400 rpm. The tensions acting vertically downwards on the tight and slack side of the belt are 1000 N and 500 N respectively. The material of the shaft is 30 C8 steel with Se= 280MPa,Su = 600MPa,kf = 1.85 FOS = 3, the diameter of the shafta) 28 mmb) 25 mmc) 32 mmd) 35 mmCorrect answer is option 'C'. Can you explain this answer?.
A pulley is supported midway between the two bearings spaced 400 mm apart on a shaft rotating at 1400 rpm. The tensions acting vertically downwards on the tight and slack side of the belt are 1000 N and 500 N respectively. The material of the shaft is 30 C8 steel with Se= 280MPa,Su = 600MPa,kf = 1.85 FOS = 3, the diameter of the shafta) 28 mmb) 25 mmc) 32 mmd) 35 mmCorrect answer is option 'C'. Can you explain this answer? 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 A pulley is supported midway between the two bearings spaced 400 mm apart on a shaft rotating at 1400 rpm. The tensions acting vertically downwards on the tight and slack side of the belt are 1000 N and 500 N respectively. The material of the shaft is 30 C8 steel with Se= 280MPa,Su = 600MPa,kf = 1.85 FOS = 3, the diameter of the shafta) 28 mmb) 25 mmc) 32 mmd) 35 mmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A pulley is supported midway between the two bearings spaced 400 mm apart on a shaft rotating at 1400 rpm. The tensions acting vertically downwards on the tight and slack side of the belt are 1000 N and 500 N respectively. The material of the shaft is 30 C8 steel with Se= 280MPa,Su = 600MPa,kf = 1.85 FOS = 3, the diameter of the shafta) 28 mmb) 25 mmc) 32 mmd) 35 mmCorrect answer is option 'C'. Can you explain this answer?.
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A pulley is supported midway between the two bearings spaced 400 mm apart on a shaft rotating at 1400 rpm. The tensions acting vertically downwards on the tight and slack side of the belt are 1000 N and 500 N respectively. The material of the shaft is 30 C8 steel with Se= 280MPa,Su = 600MPa,kf = 1.85 FOS = 3, the diameter of the shafta) 28 mmb) 25 mmc) 32 mmd) 35 mmCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for A pulley is supported midway between the two bearings spaced 400 mm apart on a shaft rotating at 1400 rpm. The tensions acting vertically downwards on the tight and slack side of the belt are 1000 N and 500 N respectively. The material of the shaft is 30 C8 steel with Se= 280MPa,Su = 600MPa,kf = 1.85 FOS = 3, the diameter of the shafta) 28 mmb) 25 mmc) 32 mmd) 35 mmCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of A pulley is supported midway between the two bearings spaced 400 mm apart on a shaft rotating at 1400 rpm. The tensions acting vertically downwards on the tight and slack side of the belt are 1000 N and 500 N respectively. The material of the shaft is 30 C8 steel with Se= 280MPa,Su = 600MPa,kf = 1.85 FOS = 3, the diameter of the shafta) 28 mmb) 25 mmc) 32 mmd) 35 mmCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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