1. Intro to Physics Units

What is the speed of a proton that has total energy $1000$ GeV?

A high-energy beam of alpha particles collides with a stationary helium gas target. What must the total energy of a beam particle be if the available energy in the collision is $16.0$ GeV?

The magnetic field in a cyclotron that accelerates protons is $1.70$ T. How many times per second should the potential across the dees reverse? (This is twice the frequency of the circulating protons.)

Deuterons in a cyclotron travel in a circle with radius $32.0$ cm just before emerging from the dees. The frequency of the applied alternating voltage is $9.00$ MHz. Find the magnetic field.

An electron with a total energy of $30.0$ GeV collides with a stationary positron. What is the available energy?

A proton and an antiproton annihilate, producing two photons. Find the energy, frequency, and wavelength of each photon if the $p$ and $\bar{p}$ are initially at rest.

Two equal-energy photons collide head-on and annihilate each other, producing a ${\text{µ}}^{+}{\text{µ}}^{-}$ pair. The muon mass is given in terms of the electron mass in Section $44.1$. Calculate the maximum wavelength of the photons for this to occur. If the photons have this wavelength, describe the motion of the ${\text{µ}}^{+}$ and immediately after they are produced.

A neutral pion at rest decays into two photons. Find the energy, frequency, and wavelength of each photon. In which part of the electromagnetic spectrum does each photon lie? (Use the pion mass given in terms of the electron mass in Section $44.1$.)

"(I) Estimate the order of magnitude (power of 10) of: 86.30 x 10³"

"(II) Use Table 1–3 to estimate the total number of protons or neutrons in the human body"

"(II) A typical atom has a diameter of about 1.0 x 10^-10 m. Approximately how many atoms are along a 1.0-cm line, assuming they just touch?"

Many sailboats are docked at a marina 4.4 km away on the opposite side of a lake. You stare at one of the sailboats because, when you are lying flat at the water's edge, you can just see its deck but none of the side of the sailboat. You then go to that sailboat on the other side of the lake and measure that the deck is 1.5 m above the level of the water. Using Fig. 1–14, where h = 1.5 m , estimate the radius R of the Earth.

Global positioning satellites (GPS) can be used to determine your position with great accuracy. If one of the satellites is 20,000 km from you, and you want to know your position to ±2 m, what percent uncertainty in the distance is required? How many significant figures are needed in the distance?

If you walked north along one of Earth's lines of longitude until you had changed latitude by 1 minute of arc (there are 60 minutes per degree), how far would you have walked (in miles)? This distance is a nautical mile (page 7).

Determine the percent uncertainty in θ, and in sin θ, when θ = 75.0° ± 0.5°.