Conceptual Questions:
1. Describe why a space voyager could reach a distant star within her lifetime while taking many thousand years as seen by people remaining back on earth.
2. List and describe the postulates of relativity.
3. According to Einstein's prediction, which of the following happens to the size of the time interval between two events occurring in an inertial frame of reference as the frame's velocity with respect to the observer increases?
a. The interval increases.
b. The interval decreases.
c. The interval remains constant.
d. The interval vanishes to zero when velocity equals speed of light.
4. According to Einstein's prediction, which of the following happens to the length of an object, measured in the dimension parallel to the motion of its inertial frame of reference, as the velocity of this frame increases with respect to a stationary observer?
a. The length increases
b. The length decreases
c. The length remains constant
d. The answer depends on the direction of motion.
5. The short lifetime of muons created in the upper atmosphere of the earth would not allow them to reach the surface of the earth unless their lifetime increased by time dilation. From the reference system of a muon, it can reach the surface of the earth because:
a. time dilation increases their velocity.
b. time dilation increases their energy.
c. length contraction decreases the distance to the earth.
d. the relativistic speed of the earth toward them is added to their velocity.
6. A boxcar without a front or a back is moving toward the right. Two flashes of light move through the boxcar, one moving from back to front toward the right, the other moving from front to back toward the left. A passenger in the boxcar records how long it takes each flash of light to pass from one end of the boxcar to the other end. According to the passenger, which took longer?
a. the flash going from back to front
b. the flash going from front to back
c. they both took the same time
d. it depends on whether the passenger is sitting at the front or the back of
the boxcar
Numerical Problems: help is at the end of the page.
1. The observed relativistic length of a spacecraft moving by the observer at 0.7 c will be what factor times that of the measured rocket length if it were at rest?
ans: 0.71
2. A proton with rest mass of 1.67 x10-27 kg moves with a speed of 0.60 c in an accelerator. What is its relativistic momentum?
ans: 3.76 x10-19 kg-m/s
3. If the rest mass of a proton is 1.67 x10-27 kg, what is the rest mass energy of the proton?
ans: 1.5 x10-10 J.
4. An astronaut at rest has a heart rate of 65 beats/min. What will her heart rate be as measured by an earth observer when the astronaut's spaceship goes by the earth at a speed of 0.6 c?
ans: 52 beats/min.
5. A spaceship of rest mass 106 kg is to be accelerated to 0.6 c. How much energy does this acceleration require?
ans: 2.25 x1022 J.
6. In a typical color television tube, the electrons are accelerated through a potential difference of 25,000 Volts. What speed do the electrons have when they strike the screen? (qe = 1.6 x10-19 C, me = 9.1 x10-31 kg)
ans: 0.30 c.
7. If astronauts could travel at v = 0.95 c, we on Earth would say it takes (4.2/0.95) = 4.4 years to reach Alpha Centauri, 4.2 lightyears away. The astronauts disagree. How much time passes on the astronaut's clocks?
ans: 1.38 years.
Help:
1. Text sec 26.3: sqrt(1-v*v/c*c)
2. Text sec 26.5: mv/sqrt(1-v*v/c*c)
3. Text sec 26.6: E = mc2
4. Text sec 26.2: Dt =
gDto (that is for PERIOD-
need invert since rate=1/period).
5. Text sec 26.6: Emotion = (g - 1)
mc2.
6. KE energy gained = qV.
Must then solve relativistic KE equation (see answer 5) for v.
7. Solve for proper time given dilated time.