26.3-26.6 Simultaneity, Time Dilation, Length Contraction, and Spacetime Diagrams
Extending life? Free neutrons have an average lifetime of about 1000 s before transforming into an electron, a proton, and an anti-neutrino. If a neutron leaves the Sun at a speed of 0.999c, (a) how long does it live according to an Earth observer? (b) Will such a neutron reach Pluto (
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- A spacecraft built in the shape of a sphere moves past an observer on the Earth with a speed of 0.500c. What shape does the observer measure for the spacecraft as it goes by? (a) a sphere (b) a cigar shape, elongated along the direction of motion (c) a round pillow shape, flattened along the direction of motion (d) a conical shape, pointing in the direction of motionarrow_forwardAn astronaut is traveling in a space vehicle moving at 0.500c relative to the Earth. The astronaut measures her pulse rate at 75.0 beats per minute. Signals generated by the astronauts pulse are radioed to the 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-based observer measure? (b) What If? What would be the pulse rate if the speed of the space vehicle were increased to 0.990c?arrow_forward(a) Calculate the relativistic quantity =11v2/c2for 1.00-TeV protons produced at Fermilab. (b) If such a proton created a +having the same speed, how long would its life be in the laboratory? (c) How far could it travel in this time?arrow_forward
- An interstellar space probe is launched from Earth. After a brief period of acceleration, it moves with a constant velocity, 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 years as measured in a rest frame. (a) How long do the batteries on the space probe last as measured by mission control on Earth? (b) How far is the probe from Earth when its batteries fail as measured by mission control? (c) How far is the probe from Earth as measured by its built-in trip odometer when its batteries fail? (d) For what total time after launch are data received from the probe by mission control? Note dial radio waves travel at the speed of light and fill the space between the probe and Earth at the time the battery fails.arrow_forward(a) How long does it take the astronaut in Example 28.2 to travel 4.30 ly at 0.99944c (as measured by the Earth-bound observer)? (b) How long does it take according to the astronaut? (c) Verify that these two times are related through time dilation with =30.00 as given.arrow_forwardImagine an astronaut on a trip to Sirius, which lies 8 light-years from Earth. Upon arrival at Sirius, the astronaut finds that the trip lasted 6 years. If the trip was made at a constant speed of 0.8c, how can the 8-light-year distance be reconciled with the 6-year duration?arrow_forward
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