Chapter 39: Problem 43

The Tevatron at Fermilab accelerates protons to energy of 1 TeV. (a) How much is this in joules? (b) How far would a 1 -g mass have to fall in Earth's gravitational field to gain this much energy?

Short Answer

Expert verified

Part (a) 1 TeV is equivalent to \(1.60217663 × 10^{-7}\) joules. Part (b) In Earth's gravitational field, a 1-gram mass would need to fall 0.016 m (or 1.6 cm) to gain this much energy.

Step by step solution

Conversion of TeV to Joules

1 electronvolt (eV) is equivalent to \(1.60217663 × 10^{-19}\) joules. As the given energy is in teraelectronvolts (TeV), which is \(10^{12}\) eV, we multiply the value of one eV in joules by \(10^{12}\) and the given energy in TeV. Therefore, 1 TeV = \(1 × 1.60217663 × 10^{-19} × 10^{12} = 1.60217663 × 10^{-7}\) joules.

Calculate Potential Energy

Firstly, potential energy (PE) is given by the formula \(PE = mgh\), where m is the mass in kilograms, g is the acceleration due to gravity (9.8 m/s² on Earth), and h is the height in meters. We are asked to find the distance (height) a 1-gram mass would have to fall, which means we have to rearrange the formula to find h: \(h = PE / (mg)\). Remember to convert 1 gram to kilograms by dividing by 1000.

Substitute and solve

The potential energy is the value derived in Step 1: \(1.60217663 × 10^{-7}\) joules. The mass m is 1 gram, which is \(0.001\) kg, and g is \(9.8 m/s²\). Applying these values into the formula gives \(h = (1.60217663 × 10^{-7})/(0.001 × 9.8) = 0.016 m\).

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The Tevatron at Fermilab accelerates protons to energy of 1 TeV. (a) How much is this in joules? (b) How far would a 1 -g mass have to fall in Earth's gravitational field to gain this much energy?

Short Answer

Step by step solution

Conversion of TeV to Joules

Calculate Potential Energy

Substitute and solve

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