Showing 1 to 20 of 3946 Questions

• A 2 000-kg car moving at 20.0 m/s collides and locks together with a 1 500-kg car at rest at a stop sign. Show that momentum is conserved in a reference frame moving at 10.0 m/s in the direction of the moving car.
• A ball is thrown at 20.0 m/s inside a boxcar moving along the tracks at 40.0 m/s. What is the speed of the ball relative to the ground if the ball is thrown?
(a) Forward
(b) Backward
(c) Out the side door?
• In a laboratory frame of reference, an observer notes that Newton’s second law is valid. Show that it is also valid for an observer moving at a constant speed, small compared with the speed of light, relative to the laboratory frame.
• Show that Newton’s second law is not valid in a reference frame moving past the laboratory frame of Problem 3 with a constant acceleration.
• How fast must a meter stick be moving if its length is measured to shrink to 0.500 m?
• At what speed does a clock move if it is measured to run at a rate that is half the rate of a clock at rest with respect to an observer?
• An astronaut is traveling in a space vehicle that has a speed of 0.500c relative to the Earth. The astronaut measures her pulse rate at 75.0 beats per minute. Signals generated by the astronaut’s pulse are radioed to Earth when the vehicle is moving in a direction perpendicular to the line that connects the vehicle with an observer on the Earth.
(a) What pulse rate does the Earth observer measure?
(b) What If? What would be the pulse rate if the speed of the space vehicle were increased to 0.990c?
• An astronomer on Earth observes a meteoroid in the southern sky approaching the Earth at a speed of 0.800c. At the time of its discovery the meteoroid is 20.0 ly from the Earth. Calculate
(a) The time interval required for the meteoroid to reach the Earth as measured by the earthbound astronomer,
(b) This time interval as measured by a tourist on the meteoroid, and
(c) The distance to the Earth as measured by the tourist.
• An atomic clock moves at 1 000 km/h for 1.00 h as measured by an identical clock on the Earth. How many nanoseconds slow will the moving clock be compared with the Earth clock, at the end of the 1.00-h interval?
• A muon formed high in the Earth’s atmosphere travels at speed v = 0.990c for a distance of 4.60 km before it decays into an electron, a neutrino, and an antineutrino (μ− → e− + v + v).
(a) How long does the muon live, as measured in its reference frame?
(b) How far does the earth travel, as measured in the frame of the muon?
• A spacecraft with a proper length of 300 m takes 0.750 μs to pass an Earth observer. Determine the speed of the spacecraft as measured by the Earth observer.
• (a) An object of proper length Lp takes a time interval ∆t to pass an Earth observer. Determine the speed of the object as measured by the Earth observer.
(b) A column of tanks, 300 m long, takes 75.0 s to pass a child waiting at a street corner on her way to school. Determine the speed of the armored vehicles.
(c) Show that the answer to part (a) includes the answer to Problem 11 as a special case, and includes the answer to part (b) as another special case.
• In 1963 Mercury astronaut Gordon Cooper orbited the Earth 22 times. The press stated that for each orbit he aged 2 millionths of a second less than he would have if he had remained on the Earth.
(a) Assuming that he was 160 km above the Earth in a circular orbit, determine the time difference between someone on the Earth and the orbiting astronaut for the 22 orbits. You will need to use the approximation √1 – x ≈ 1 – x/2, for small x.
(b) Did the press report accurate information? Explain.
• A friend passes by you in a spacecraft traveling at a high speed. He tells you that his craft is 20.0 m long and that the identically constructed craft you are sitting in is 19.0 m long. According to your observations,
(a) How long is your spacecraft?
(b) How long is your friend’s craft, and
(c) What is the speed of your friend’s craft?
• The identical twins Speedo and Goslo join a migration from the Earth to Planet X. It is 20.0 ly away in a reference frame in which both planets are at rest. The twins, of the same age, depart at the same time on different spacecraft. Speedo’s craft travels steadily at 0.950c and Goslo’s at 0.750c. Calculate the age difference between the twins after Goslo’s spacecraft lands on Planet X. Which twin is the older?
• An interstellar space probe is launched from the Earth. After a brief period of acceleration it moves with a constant velocity, with a magnitude of 70.0% of the speed of light. Its nuclear-powered batteries supply the energy to keep its data transmitter active continuously. The batteries have a lifetime of 15.0 yr as measured in a rest frame.
(a) How long do the batteries on the space probe last as measured by Mission Control on the Earth?
(b) How far is the probe from the Earth when its batteries fail, as measured by Mission Control?
(c) How far is the probe from the Earth when its batteries fail, as measured by its built-in trip odometer?
(d) For what total time interval after launch are data received from the probe by Mission Control? Note that radio waves travel at the speed of light and fill the space between the probe and the Earth at the time of battery failure.
• An alien civilization occupies a brown dwarf, nearly stationary relative to the Sun, several light years away. The extraterrestrials have come to love original broadcasts of I Love Lucy, on our television channel 2, at carrier frequency 57.0 MHz. Their line of sight to us is in the plane of the Earth’s orbit. Find the difference between the highest and lowest frequencies they receive due to the Earth’s orbital motion around the Sun.
• Police radar detects the speed of a car (Fig. P39.19) as follows. Microwaves of a precisely known frequency are broadcast toward the car. The moving car reflects the microwaves with a Doppler shift. The reflected waves are received and combined with an attenuated version of the transmitted wave. Beats occur between the two microwave signals. The beat frequency is measured.
(a) For an electromagnetic wave reflected back to its source from a mirror approaching at speed v, show that the reflected f=fsource c + v/ c – v where fsource is the source frequency.
(b) When v is much less than c, the beat frequency is much smaller than the transmitted frequency. In this case use the approximation f + fsource + 2 fsource and show that the beat frequency can be written as fbeat = 2v/A).
(c) What beat frequency is measured for a car speed of 30.0 m/s if the microwaves have frequency 10.0 GHz?
(d) If the beat frequency measurement is accurate to +5 Hz, how accurate is the velocity measurement?

• The red shift A light source recedes from an observer with a speed vsource that is small compared with c.
(a) Show that the fractional shift in the measured wavelength is given by the approximate expression ∆A/A ≈ vsource/c this phenomenon is known as the red shift, because the visible light is shifted toward the red.
(b) Spectroscopic measurements of light at A = 397 nm coming from a galaxy in Ursa Major reveal a red shift of 20.0 nm. What is the recessional speed of the galaxy?
• A physicist drives through a stop light. When he is pulled over, he tells the police officer that the Doppler shift made the red light of wavelength 650 nm appear green to him, with a wavelength of 520 nm. The police officer writes out a traffic citation for speeding. How fast was the physicist traveling, according to his own testimony?
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