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In a belt drive the centrifugal tension is 1 kN. The ratio of tensions is 2 and runs at a linear speed of 10 m/s and has to transmits 20 kW. What should be the initial tension?
- a)4 kN
- b)3 kN
- c)2 kN
- d)2.5 kN
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
In a belt drive the centrifugal tension is 1 kN. The ratio of tensions...
Given:
Centrifugal tension = 1 kN, Ratio of tensions = 2, Linear speed = 10 m/s, Power to be transmitted = 20 kW
To find: Initial tension in the belt drive
Formula:
Centrifugal tension = m*v^2/r, where m = mass of belt per unit length, v = linear speed, r = radius of pulley
Tension ratio = T2/T1 = e^(μθ), where μ = coefficient of friction, θ = angle of lap
Power transmitted = T1*v
Explanation:
1. Finding the mass of the belt per unit length
Centrifugal tension = m*v^2/r
1 kN = m*(10 m/s)^2/r
m = 1*10^3* r/100
2. Finding the angle of lap
Tension ratio = T2/T1 = e^(μθ)
2 = e^(μθ)
Taking natural logarithm on both sides,
ln(2) = μθ
θ = ln(2)/μ
3. Finding the initial tension
Using the formula, Power transmitted = T1*v,
20 kW = T1*10 m/s
T1 = 2*10^3 N
From the equation Tension ratio = T2/T1 = 2,
T2 = 2*T1 = 4 kN
The initial tension in the belt drive = T1 + T2 + Centrifugal tension
= 2*10^3 N + 4*10^3 N + 1 kN
= 7*10^3 N = 7 kN
Therefore, the correct option is A) 4 kN.
Centrifugal tension = 1 kN, Ratio of tensions = 2, Linear speed = 10 m/s, Power to be transmitted = 20 kW
To find: Initial tension in the belt drive
Formula:
Centrifugal tension = m*v^2/r, where m = mass of belt per unit length, v = linear speed, r = radius of pulley
Tension ratio = T2/T1 = e^(μθ), where μ = coefficient of friction, θ = angle of lap
Power transmitted = T1*v
Explanation:
1. Finding the mass of the belt per unit length
Centrifugal tension = m*v^2/r
1 kN = m*(10 m/s)^2/r
m = 1*10^3* r/100
2. Finding the angle of lap
Tension ratio = T2/T1 = e^(μθ)
2 = e^(μθ)
Taking natural logarithm on both sides,
ln(2) = μθ
θ = ln(2)/μ
3. Finding the initial tension
Using the formula, Power transmitted = T1*v,
20 kW = T1*10 m/s
T1 = 2*10^3 N
From the equation Tension ratio = T2/T1 = 2,
T2 = 2*T1 = 4 kN
The initial tension in the belt drive = T1 + T2 + Centrifugal tension
= 2*10^3 N + 4*10^3 N + 1 kN
= 7*10^3 N = 7 kN
Therefore, the correct option is A) 4 kN.
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In a belt drive the centrifugal tension is 1 kN. The ratio of tensions is 2 and runs at a linear speed of 10 m/s and has to transmits 20 kW. What should be the initial tension?a)4 kNb)3 kNc)2 kNd)2.5 kNCorrect answer is option 'A'. Can you explain this answer?
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