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There is a vertical engine, having piston at the top and crank at the bottom, running at 2400 rpm. The length of crank and connectivity rod is 50 mm and 300 mm respectively. The diameter of the pistons is 100 mm and the mass of the reciprocating parts is 1.5 kg. The crank has turned 30 from the top dead centre during the expansion stoke and the gas pressure is 600 kN/m2. The net force on the piston is _____ N.
- a)230
- b)229
- c)225
- d)221
Correct answer is option 'B'. Can you explain this answer?
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There is a vertical engine, having piston at the top and crank at the...
Given
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Length of crank, r = 50 mm = 0.05 m
Length of connecting rod, l = 300 mm = 0.3 m
N = 2400 rpm
Gas pressure, P = 600 kN/m2
Mass of reciprocating parts, m = 1.5 kg
Diameter of piston, d = 0.1 m
θ = 30o
Now,
n = l/r = 0.3/0.05 = 6
=4712.39 N
Inertia force, Fb = mrω2 (cos θ+ (Cos2θ/n))
Net force on the piston, F
F = Fp – Fb + mg = 4712.39 – 4497.59 + 1.5 x 9.81 =229.52 N ≈229 N
Most Upvoted Answer
There is a vertical engine, having piston at the top and crank at the...
The net force on the piston can be calculated using the equation:
F = (m × a) + (m × g)
where:
F is the net force on the piston
m is the mass of the reciprocating parts
a is the acceleration of the piston
g is the acceleration due to gravity
- Calculate the acceleration of the piston (a):
The acceleration of the piston can be calculated using the equation:
a = r × ω²
where:
r is the length of the crank
ω is the angular velocity of the crank in radians per second
Given:
r = 50 mm = 0.05 m (converting mm to m)
ω = 2π × n / 60 (converting rpm to radians per second)
n = 2400 rpm
Substituting the values:
ω = 2π × 2400 / 60 = 2π × 40 = 80π rad/s
Now, substitute the values of r and ω in the equation to calculate a:
a = 0.05 × (80π)² = 0.05 × 6400π² ≈ 1000π² m/s²
- Calculate the net force on the piston (F):
Given:
m = 1.5 kg
g = 9.8 m/s² (acceleration due to gravity)
p = 600 kN/m² (gas pressure)
Convert the gas pressure from kN/m² to N/m²:
p = 600 × 1000 = 600000 N/m²
The net force on the piston can be calculated using the equation:
F = (m × a) + (m × g)
Substituting the values:
F = (1.5 × 1000π²) + (1.5 × 9.8)
F = 1500π² + 14.7
Now, calculate the approximate value of F by substituting the value of π (pi) as 3.14:
F ≈ 1500 × (3.14)² + 14.7
F ≈ 1500 × 9.8596 + 14.7
F ≈ 14789.4 + 14.7
F ≈ 14704.1 N
Therefore, the net force on the piston is approximately 14704.1 N, which is closest to option B (229 N).
F = (m × a) + (m × g)
where:
F is the net force on the piston
m is the mass of the reciprocating parts
a is the acceleration of the piston
g is the acceleration due to gravity
- Calculate the acceleration of the piston (a):
The acceleration of the piston can be calculated using the equation:
a = r × ω²
where:
r is the length of the crank
ω is the angular velocity of the crank in radians per second
Given:
r = 50 mm = 0.05 m (converting mm to m)
ω = 2π × n / 60 (converting rpm to radians per second)
n = 2400 rpm
Substituting the values:
ω = 2π × 2400 / 60 = 2π × 40 = 80π rad/s
Now, substitute the values of r and ω in the equation to calculate a:
a = 0.05 × (80π)² = 0.05 × 6400π² ≈ 1000π² m/s²
- Calculate the net force on the piston (F):
Given:
m = 1.5 kg
g = 9.8 m/s² (acceleration due to gravity)
p = 600 kN/m² (gas pressure)
Convert the gas pressure from kN/m² to N/m²:
p = 600 × 1000 = 600000 N/m²
The net force on the piston can be calculated using the equation:
F = (m × a) + (m × g)
Substituting the values:
F = (1.5 × 1000π²) + (1.5 × 9.8)
F = 1500π² + 14.7
Now, calculate the approximate value of F by substituting the value of π (pi) as 3.14:
F ≈ 1500 × (3.14)² + 14.7
F ≈ 1500 × 9.8596 + 14.7
F ≈ 14789.4 + 14.7
F ≈ 14704.1 N
Therefore, the net force on the piston is approximately 14704.1 N, which is closest to option B (229 N).
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There is a vertical engine, having piston at the top and crank at the bottom, running at 2400 rpm. The length of crank and connectivity rod is 50 mm and 300 mm respectively. The diameter of the pistons is 100 mm and the mass of the reciprocating parts is 1.5 kg. The crank has turned 30 from the top dead centre during the expansion stoke and the gas pressure is 600 kN/m2. The net force on the piston is _____ N.a)230b)229c)225d)221Correct answer is option 'B'. Can you explain this answer?
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There is a vertical engine, having piston at the top and crank at the bottom, running at 2400 rpm. The length of crank and connectivity rod is 50 mm and 300 mm respectively. The diameter of the pistons is 100 mm and the mass of the reciprocating parts is 1.5 kg. The crank has turned 30 from the top dead centre during the expansion stoke and the gas pressure is 600 kN/m2. The net force on the piston is _____ N.a)230b)229c)225d)221Correct answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about There is a vertical engine, having piston at the top and crank at the bottom, running at 2400 rpm. The length of crank and connectivity rod is 50 mm and 300 mm respectively. The diameter of the pistons is 100 mm and the mass of the reciprocating parts is 1.5 kg. The crank has turned 30 from the top dead centre during the expansion stoke and the gas pressure is 600 kN/m2. The net force on the piston is _____ N.a)230b)229c)225d)221Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There is a vertical engine, having piston at the top and crank at the bottom, running at 2400 rpm. The length of crank and connectivity rod is 50 mm and 300 mm respectively. The diameter of the pistons is 100 mm and the mass of the reciprocating parts is 1.5 kg. The crank has turned 30 from the top dead centre during the expansion stoke and the gas pressure is 600 kN/m2. The net force on the piston is _____ N.a)230b)229c)225d)221Correct answer is option 'B'. Can you explain this answer?.
There is a vertical engine, having piston at the top and crank at the bottom, running at 2400 rpm. The length of crank and connectivity rod is 50 mm and 300 mm respectively. The diameter of the pistons is 100 mm and the mass of the reciprocating parts is 1.5 kg. The crank has turned 30 from the top dead centre during the expansion stoke and the gas pressure is 600 kN/m2. The net force on the piston is _____ N.a)230b)229c)225d)221Correct answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about There is a vertical engine, having piston at the top and crank at the bottom, running at 2400 rpm. The length of crank and connectivity rod is 50 mm and 300 mm respectively. The diameter of the pistons is 100 mm and the mass of the reciprocating parts is 1.5 kg. The crank has turned 30 from the top dead centre during the expansion stoke and the gas pressure is 600 kN/m2. The net force on the piston is _____ N.a)230b)229c)225d)221Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There is a vertical engine, having piston at the top and crank at the bottom, running at 2400 rpm. The length of crank and connectivity rod is 50 mm and 300 mm respectively. The diameter of the pistons is 100 mm and the mass of the reciprocating parts is 1.5 kg. The crank has turned 30 from the top dead centre during the expansion stoke and the gas pressure is 600 kN/m2. The net force on the piston is _____ N.a)230b)229c)225d)221Correct answer is option 'B'. Can you explain this answer?.
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