(a)
The angle between the invar bars.
(a)
Answer to Problem 54AP
The angle between the invar bars is
Explanation of Solution
The diagram for the three metal bars is depicted below.
Write the equation angle from trigonometry.
Here,
Write the equation for the final length.
Here,
Conclusion:
Substitute
Thus, the angle between the invar bars is
(b)
The value of angle is accurate for both negative and positive temperature or not.
(b)
Answer to Problem 54AP
Yes, the value of angle is accurate for both negative and positive temperature.
Explanation of Solution
If the temperature difference positive or negative, it will not affect the value of angle.
If the temperature is positive, the bar will expand. As well as the temperature i negative, the bar will have contraction.
Thus, the value of angle is accurate for both negative and positive temperature.
(c)
The value of angle is accurate for zero degree temperature or not.
(c)
Answer to Problem 54AP
Yes, the value of angle is accurate for zero degree temperature.
Explanation of Solution
Write the expression for the angle.
At,
Thus, the value of angle is accurate for zero degree temperature.
(d)
The angle between the invar bars when the invar also expand.
(d)
Answer to Problem 54AP
The angle between the invar bars when the invar also expand is
Explanation of Solution
Refer Figure 1.
Write the equation angle from trigonometry.
Here,
Write the equation for the final length of the aluminium.
Here,
Write the equation for the final length of the invar.
Here,
Conclusion:
Substitute
Thus, the angle between the invar bars when the invar also expand is
(e)
The greatest value of angle between the invar bars.
(e)
Answer to Problem 54AP
The greatest value of angle between the invar bars is
Explanation of Solution
Write the equation for the angle
Conclusion:
Substitute
Thus, the greatest value of angle between the invar bars is
(f)
The smallest value of angle between the invar bars.
(f)
Answer to Problem 54AP
The smallest value of angle between the invar bars is
Explanation of Solution
Write the equation for the angle
Conclusion:
Substitute
Thus, The smallest value of angle between the invar bars is
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Chapter 19 Solutions
Physics for Scientists and Engineers With Modern Physics
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