Problem 2-1 In the following, consider a system of units where time is measured in seconds (s) and mass in kilograms (kg), just like the SI system, but length is measured in units

Problem 2-1 In the following, consider a system of units where time is measured in seconds (s)
and mass in kilograms (kg), just like the SI system, but length is measured in units
of “lightrseconds”, also denoted by s, the distance ljght travels in 1 s. In this “rela~
tivistic" system of units (call it the “SR" system), the speed of light is c = 1 and all
other speeds 1) are similarly dimensionless, representing the fraction v/c. a. What is the diameter of the earth in seconds? b A sign on a hiking trail reads “Viewpoint: 55 us". About how long would it
take you to walk to that viewpoint? (1 us : 10’6 s) PHY 317L 2 c A sign on the highway reads “Speed Limit 6 X 10—5 “. Translate this into miles
per hour. d, The Voyager spacecraft achieved speeds in excess of 72,000 km/hr relative to
earth. What is this speed in SR units‘.7 e, Show that in the SR system, mass, momentum (Newtonian momentum: p =
my) and kinetic enery (Newtonian kinetic enery: E : %mv2) are all measured
in kilograms. Imagine a large truck with a mass of 25 metric tons (25,000 kg) is
traveling at a speed of 95 km/hr. What are its momentum and kinetic energy
expressed in SR units? f. In the SI system, power is measured in watts (1W = lJ/s = 1kg ‘ m’s’a). What
are the dimensions of the natural unit for powerch it a ”Superwattkin the
SR system‘.7 A typical large electrical generator produces about 1 GW = 109 W
of electrical power. What is this in Superwatts? gr What are the dimensions of the natural unit of acceleration in the SR system?
Express the magnitude of one unit of acceleration in the SR system in terms of
g, the acceleration due to gravity at the earth‘s surface.

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