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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 \(1.60217663 脳 10^{-7}\) 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

01

Conversion of TeV to Joules

1 electronvolt (eV) is equivalent to \(1.60217663 脳 10^{-19}\) 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 = \(1 脳 1.60217663 脳 10^{-19} 脳 10^{12} = 1.60217663 脳 10^{-7}\) joules.
02

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/s虏 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.
03

Substitute and solve

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

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Potential Energy
Potential energy is the energy stored in an object due to its position or configuration. One of the most common types of potential energy is gravitational potential energy, which depends on an object's height above the ground.
  • The formula for gravitational potential energy is: \(PE = mgh\), where \(m\) is mass, \(g\) is gravitational acceleration, and \(h\) is height.
  • Potential energy is a scalar quantity, meaning it only has magnitude, not direction.
Potential energy conversion is a fundamental concept in physics as it explains how energy is transformed from one form to another.
Fermilab Tevatron
The Fermilab Tevatron was one of the most powerful particle accelerators in the world. It was located in Batavia, Illinois, and was in operation until 2011. In this ring-shaped facility, particles like protons were accelerated to incredibly high speeds.
  • The Tevatron reached energies as high as 1 teraelectronvolt (TeV).
  • This high energy was crucial for experiments in particle physics, helping scientists study fundamental particles.
Although the Tevatron is no longer operational, its contributions to science continue to be significant.
Electronvolt to Joules Conversion
An electronvolt (eV) is a unit of energy commonly used in the field of particle physics. Converting eV to joules is necessary to understand energy values in standard scientific units.
  • 1 eV is equivalent to \(1.60217663 \times 10^{-19}\) joules.
  • A teraelectronvolt (TeV) is \(10^{12}\) eV. Therefore, to convert TeV to joules, multiply by this conversion factor.
  • For example, 1 TeV equals \(1.60217663 \times 10^{-7}\) joules.
Understanding this conversion helps bridge the gap between different scientific disciplines.
Gravitational Potential Energy
Gravitational potential energy (GPE) is energy an object possesses due to its position in a gravitational field. The higher the object, the more potential energy it has.
  • The formula for GPE is \(PE = mgh\), where \(m\) is mass in kilograms, \(g\) is the acceleration due to gravity, and \(h\) is height in meters.
  • On Earth, \(g\) is approximately \(9.8 \text{ m/s}^2\).
  • GPE plays a key role in various physics problems, such as calculating the energy required for an object to reach a certain height.
Gravitational potential energy is a critical concept for understanding motion and energy transfer.

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Most popular questions from this chapter

Pions are the lightest mesons, with mass some 270 times that of the electron. Charged pions decay typically into a muon and a neutrino or antineutrino. This makes pion beams useful for producing beams of neutrinos, which physicists use to study those elusive particles. In a medical application during the late 20 th century, accelerator centers installed "biomedical beam lines" to test pions for cancer therapy. In these experiments, pions attached themselves to atomic nuclei within cancer cells. The nuclei would literally explode, delivering a "pion star" of cancer-killing nuclear debris. Unfortunately, results were not as encouraging as hoped, and enthusiasm for this technique has waned. The quark composition of the negative pion is a. uud. b. \(d \bar{u}\) c. ud. d. \(c \bar{c}\)

The \(\eta^{0}\) particle is a neutral nonstrange meson that can decay to a positive pion, a negative pion, and a neutral pion. Write the reaction for this decay, and verify that it conserves charge, baryon number, and strangeness.

(a) By what factor must the magnetic field in a proton synchrotron be increased as the proton energy increases by a factor of \(10 ?\) Assume the protons are highly relativistic, so \(\gamma \gg 1\). (b) By what factor must the diameter of the accelerator be increased to raise the energy by a factor of 10 without changing the magnetic field?

Why do we need higher-energy particle accelerators to explore fully the standard model?

Consider systems described by wave functions that are proportional to the terms (a) \(x y^{2} z,\) (b) \(x^{2} y z\), and (c) \(x y z,\) where \(x, y,\) and \(z\) are the spatial coordinates. Which pairs of these systems could be transformed into each other under a parity-conserving interaction?
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