BackSteel train rails are laid in 12.0-m-long segments placed end to end. The rails are laid on a winter day when their temperature is -9.0°C. How much space must be left between adjacent rails if they are just to touch on a summer day when their temperature is 33.0°C?
As a new mechanical engineer for Engines Inc., you have been assigned to design brass pistons to slide inside steel cylinders. The engines in which these pistons will be used will operate between 20.0°C and 150.0°C. Assume that the coefficients of expansion are constant over this temperature range. If the piston just fits inside the chamber at 20.0°C, will the engines be able to run at higher temperatures? Explain.
A horizontal steel I-beam of a cross-sectional area of 0.041 m² is rigidly connected to two fixed vertical supports. If the beam was installed when the temperature was 25°C, is the ultimate strength of the steel exceeded?
(II) To what temperature would you have to heat a brass rod for it to be 1.5% longer than it is at 22°C?
At room temperature (20°C), a 5.0-cm-long brass rod is 20 μm too long to fit into a slot. To what temperature should you cool the rod so that it just barely fits?
What stress is developed if the concrete beam has a cross-sectional area of 0.15m2? Will it fracture?
A brass rod is 185 cm long and 1.60 cm in diameter. What force must be applied to each end of the rod to prevent it from contracting when it is cooled from 120.0°C to 10.0°C?
A copper wire sags 54.0 cm between two utility poles 30.0 m apart when the temperature is -15° C. Estimate the amount of sag when the temperature is + 35° C. [Hint: An estimate can be made by assuming the shape of the wire is approximately an arc of a circle; hard equations can sometimes be solved by guessing values.]
If a steel band were to fit snugly around the Earth’s equator at 25°C but then was heated to 55°C, how high above the Earth would the band be (assume equal everywhere)?
If a fluid is contained in a long narrow vessel so it can expand in essentially one direction only, show that the effective coefficient of linear expansion α is approximately equal to the coefficient of volume expansion β.
(II) To make a secure fit, rivets that are larger than the rivet hole are often used and the rivet is cooled (usually in dry ice) before it is placed in the hole. A steel rivet 1.872 cm in diameter is to be placed in a hole 1.870 cm in diameter in a metal at 24°C. To what temperature must the rivet be cooled if it is to fit in the hole?