A healthy astronaut’s heart rate is 60 beats/min . Flight doctors on Earth can monitor an astronaut’s vital signs remotely while in flight. How fast would an astronaut be flying away from Earth if the doctor measured her heart rate as 52 beats/min?

An atomic clock is taken to the North Pole, while another stays at the Equator. How far will they be out of synchronization after 1.5 years has elapsed? [Hint: Use the binomial expansion, Appendix A–2.]

How much energy would be required to break a helium nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and neutral helium are, respectively, 1.00783 u, 1.00867 u, and 4.00260 u. (This energy difference is called the total binding energy of the ${}_2^4\text{He}$ nucleus.)

The Sun radiates energy at a rate of about 4 x 10²⁶ W.

(a) At what rate is the Sun’s mass decreasing?

(b) How long does it take for the Sun to lose a mass equal to that of Earth?

(c) Estimate how long the Sun could last if it radiated constantly at this rate.

A spaceship moving toward Earth at 0.65c transmits radio signals at 95.0 MHz. At what frequency should Earth receivers be tuned?

What minimum amount of electromagnetic energy is needed to produce an electron and a positron together? A positron is a particle with the same mass as an electron, but has the opposite charge. (Note that electric charge is conserved in this process. See Section 37–5.)

An electron (m = 9.11 x 10⁻³¹ kg) is accelerated from rest to speed v by a conservative force. In this process, its potential energy decreases by 7.20 x 10⁻¹⁴ J . Determine the electron’s speed, v.