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Two cutting tools with tool life equations given below are being compared: Tool 1: VT0.1=150 Tool 2: VT0.3=300 Where V is cutting speed in m/minute and T is tool life in minutes. The breakeven cutting speed beyond which Tool 2 will have a higher tool life is ________ m/minute.
Correct answer is between '105,107'. Can you explain this answer?
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Two cutting tools with tool life equations given below are being compa...
At Breakeven point
T1 = T2
T1 = T2
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Two cutting tools with tool life equations given below are being compa...
Given tool life equations:
Tool 1: VT^0.1 = 150
Tool 2: VT^0.3 = 300
To find the breakeven cutting speed beyond which Tool 2 will have a higher tool life, we need to determine the cutting speed at which both tools will have the same tool life. Let's solve the tool life equations for the breakeven point.
1. Find the breakeven cutting speed:
Setting the tool life equations equal to each other:
VT^0.1 = VT^0.3
Taking the natural logarithm of both sides:
ln(VT^0.1) = ln(VT^0.3)
Using the logarithmic property log(a^b) = b*log(a):
0.1*ln(VT) = 0.3*ln(VT)
Dividing both sides by ln(VT):
0.1 = 0.3
This equation is not possible, as 0.1 is not equal to 0.3. Therefore, there is no cutting speed at which both tools will have the same tool life.
2. Determine the cutting speed beyond which Tool 2 will have a higher tool life:
To compare the tool lives of Tool 1 and Tool 2, we can consider a range of cutting speeds and calculate the tool life for each tool.
Let's compare the tool lives at different cutting speeds:
For Tool 1:
V = 100 m/minute, T = (150/100)^10 = 150 minutes
V = 200 m/minute, T = (150/200)^10 = 56.25 minutes
V = 300 m/minute, T = (150/300)^10 = 25 minutes
V = 400 m/minute, T = (150/400)^10 = 11.18 minutes
For Tool 2:
V = 100 m/minute, T = (300/100)^10 = 590.49 minutes
V = 200 m/minute, T = (300/200)^10 = 118.1 minutes
V = 300 m/minute, T = (300/300)^10 = 27.99 minutes
V = 400 m/minute, T = (300/400)^10 = 6.64 minutes
From the calculations, we can observe that Tool 2 has a higher tool life than Tool 1 at all cutting speeds. Therefore, there is no specific cutting speed beyond which Tool 2 will have a higher tool life. The correct answer cannot be determined as the given tool life equations do not intersect.
In conclusion, the given tool life equations do not have a breakeven point, and Tool 2 has a higher tool life than Tool 1 at all cutting speeds.
Tool 1: VT^0.1 = 150
Tool 2: VT^0.3 = 300
To find the breakeven cutting speed beyond which Tool 2 will have a higher tool life, we need to determine the cutting speed at which both tools will have the same tool life. Let's solve the tool life equations for the breakeven point.
1. Find the breakeven cutting speed:
Setting the tool life equations equal to each other:
VT^0.1 = VT^0.3
Taking the natural logarithm of both sides:
ln(VT^0.1) = ln(VT^0.3)
Using the logarithmic property log(a^b) = b*log(a):
0.1*ln(VT) = 0.3*ln(VT)
Dividing both sides by ln(VT):
0.1 = 0.3
This equation is not possible, as 0.1 is not equal to 0.3. Therefore, there is no cutting speed at which both tools will have the same tool life.
2. Determine the cutting speed beyond which Tool 2 will have a higher tool life:
To compare the tool lives of Tool 1 and Tool 2, we can consider a range of cutting speeds and calculate the tool life for each tool.
Let's compare the tool lives at different cutting speeds:
For Tool 1:
V = 100 m/minute, T = (150/100)^10 = 150 minutes
V = 200 m/minute, T = (150/200)^10 = 56.25 minutes
V = 300 m/minute, T = (150/300)^10 = 25 minutes
V = 400 m/minute, T = (150/400)^10 = 11.18 minutes
For Tool 2:
V = 100 m/minute, T = (300/100)^10 = 590.49 minutes
V = 200 m/minute, T = (300/200)^10 = 118.1 minutes
V = 300 m/minute, T = (300/300)^10 = 27.99 minutes
V = 400 m/minute, T = (300/400)^10 = 6.64 minutes
From the calculations, we can observe that Tool 2 has a higher tool life than Tool 1 at all cutting speeds. Therefore, there is no specific cutting speed beyond which Tool 2 will have a higher tool life. The correct answer cannot be determined as the given tool life equations do not intersect.
In conclusion, the given tool life equations do not have a breakeven point, and Tool 2 has a higher tool life than Tool 1 at all cutting speeds.
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Two cutting tools with tool life equations given below are being compared: Tool 1: VT0.1=150 Tool 2: VT0.3=300 Where V is cutting speed in m/minute and T is tool life in minutes. The breakeven cutting speed beyond which Tool 2 will have a higher tool life is ________ m/minute.Correct answer is between '105,107'. Can you explain this answer?
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Two cutting tools with tool life equations given below are being compared: Tool 1: VT0.1=150 Tool 2: VT0.3=300 Where V is cutting speed in m/minute and T is tool life in minutes. The breakeven cutting speed beyond which Tool 2 will have a higher tool life is ________ m/minute.Correct answer is between '105,107'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Two cutting tools with tool life equations given below are being compared: Tool 1: VT0.1=150 Tool 2: VT0.3=300 Where V is cutting speed in m/minute and T is tool life in minutes. The breakeven cutting speed beyond which Tool 2 will have a higher tool life is ________ m/minute.Correct answer is between '105,107'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two cutting tools with tool life equations given below are being compared: Tool 1: VT0.1=150 Tool 2: VT0.3=300 Where V is cutting speed in m/minute and T is tool life in minutes. The breakeven cutting speed beyond which Tool 2 will have a higher tool life is ________ m/minute.Correct answer is between '105,107'. Can you explain this answer?.
Two cutting tools with tool life equations given below are being compared: Tool 1: VT0.1=150 Tool 2: VT0.3=300 Where V is cutting speed in m/minute and T is tool life in minutes. The breakeven cutting speed beyond which Tool 2 will have a higher tool life is ________ m/minute.Correct answer is between '105,107'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Two cutting tools with tool life equations given below are being compared: Tool 1: VT0.1=150 Tool 2: VT0.3=300 Where V is cutting speed in m/minute and T is tool life in minutes. The breakeven cutting speed beyond which Tool 2 will have a higher tool life is ________ m/minute.Correct answer is between '105,107'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two cutting tools with tool life equations given below are being compared: Tool 1: VT0.1=150 Tool 2: VT0.3=300 Where V is cutting speed in m/minute and T is tool life in minutes. The breakeven cutting speed beyond which Tool 2 will have a higher tool life is ________ m/minute.Correct answer is between '105,107'. Can you explain this answer?.
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Two cutting tools with tool life equations given below are being compared: Tool 1: VT0.1=150 Tool 2: VT0.3=300 Where V is cutting speed in m/minute and T is tool life in minutes. The breakeven cutting speed beyond which Tool 2 will have a higher tool life is ________ m/minute.Correct answer is between '105,107'. Can you explain this answer?, a detailed solution for Two cutting tools with tool life equations given below are being compared: Tool 1: VT0.1=150 Tool 2: VT0.3=300 Where V is cutting speed in m/minute and T is tool life in minutes. The breakeven cutting speed beyond which Tool 2 will have a higher tool life is ________ m/minute.Correct answer is between '105,107'. Can you explain this answer? has been provided alongside types of Two cutting tools with tool life equations given below are being compared: Tool 1: VT0.1=150 Tool 2: VT0.3=300 Where V is cutting speed in m/minute and T is tool life in minutes. The breakeven cutting speed beyond which Tool 2 will have a higher tool life is ________ m/minute.Correct answer is between '105,107'. Can you explain this answer? theory, EduRev gives you an
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