Physicists and engineers from around the world came together to build the largest accelerator in the world, the Large Hadron Col
lider (LHC) at the CERN Laboratory in Geneva, Switzerland. The machine accelerates protons to high kinetic energies in an underground ring 27 km in circumference. What is the speed v of a proton in the LHC if the proton’s kinetic energy is 7.0 TeV? (Because v is very close to c, write v=(1−Δ)cv=(1−Δ)c and give your answer in terms of ΔΔ.)
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Answer:
The temperature must the ring be heated so that the sphere can just slip through is 106.165 °C.
Explanation:
For brass:
Radius = 1.3590 cm
Initial temperature = 23.0 °C
The sphere of radius 1.3611 cm must have to slip through the brass. Thus, on heating the brass must have to attain radius of 1.3611 cm
So,
Δ r = 1.3611 cm - 1.3590 cm = 0.0021 cm
<u>The linear thermal expansion coefficient of a metal is the ratio of the change in the length per 1 degree temperature to its length.</u>
<u>Thermal expansion for brass = 19×10⁻⁶ °C⁻¹</u>
Thus,
Also,
So,
Solving for final temperature as:
<u>Final temperature = 106.165 °C</u>