What are the rest energy, the kinetic energy, and the total energy of a 1.0 g particle with a speed of 0.80c?

(II) Estimate the number of jelly beans in the jar of Fig. 1–13.

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Recent findings in astrophysics suggest that the observable universe can be modeled as a sphere of radius R = 13.7 x 10⁹ light-years = 13.0 x 10²⁵ m with an average total mass density of about 1 x 10⁻^-26 kg/m³. Only about 4% of total mass is due to 'ordinary' matter (such as protons, neutrons, and electrons). Estimate how much ordinary matter (in kg) there is in the observable universe. (For the light-year, see Problem 25.)

(II) The diameter of the planet Mercury is 4879 km. What is the surface area of Mercury?

One mole of atoms consists of 6.02 x 10²³ individual atoms. If a mole of atoms were spread uniformly over the Earth's surface, how many atoms would there be per square meter?

Relativistic Baseball. Calculate the magnitude of the force required to give a 0.145 kg baseball an acceleration a = 1.00 m/s² in the direction of the baseball's initial velocity when this velocity has a magnitude of (a) 10.0 m/s; (c) 0.990c.

A proton (rest mass $1.67\times {10}^{-27}$ kg) has total energy that is $4.00$ times its rest energy. What are (a) the kinetic energy of the proton; (b) the magnitude of the momentum of the proton; (c) the speed of the proton?

Electrons are accelerated through a potential difference of $750$ kV, so that their kinetic energy is $7.50\times {10}^5$ eV.

(a) What is the ratio of the speed $v$ of an electron having this energy to the speed of light, $c$?

(b) What would the speed be if it were computed from the principles of classical mechanics?

A particle has rest mass $6.64\times {10}^{-27}$ kg and momentum $2.10\times {10}^{-18}$ kgm/s.

(a) What is the total energy (kinetic plus rest energy) of the particle?

(b) What is the kinetic energy of the particle?

(c) What is the ratio of the kinetic energy to the rest energy of the particle?