2. (a) (b) The starship Enterprise flies past Mars and has a KINETIC energy that is 3.00 times the rest energy of the starship. What is the speed v of the spaceship? Find v/c, then find v. Note: c is the speed of light. Inside the spaceship, a pendulum is swinging. Each swing takes 1.60 seconds as measured by the Star Trek crew performing an experiment inside the spaceship. How long will each swing take as measured by a technician at mission control on MARS watching that experiment?

(a) Using data from Table 7.1, find the mass destroyed when the energy in a barrel of crude oil is released. (b) Given these barrels contain 200 liters and assuming the density of crude oil is 750 kg/m3, what is the ratio of mass destroyed to original mass, m/m ?

(a) How long would the mum] in Example 5.3 have lived as observed on Earth if its velocity was. 0.0500c? (b) How far would it have traveled as observed on Earth? (c) What distance is this in the muon’s frame?

(a) How fast would an athlete need to be running for a 100-m race to look 100 yd long? (b) Is the answer consistent with the fact that relativistic effects are difficult to observe in ordinary circumstances? Explain.

A neutron lives 900 s when at rest relative to an observer. How fast is the neutron moving relative to an observer who measures its life span to be 2065 s?

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.

(a) All but the closest galaxies are receding from our own Milky Way Galaxy. If a galaxy 12.0x109ly away is receding from us at 0.900c, at what velocity relative to us must we send an exploratory probe to approach the other galaxy at 0.990c as measured from that galaxy? (b) How long will it take the probe to reach the other galaxy as measured from Earth? You may assume that the velocity of the other galaxy remains constant. (c) How long will it then take for a radio signal to be beamed back? (All of this is possible in principle, but not practical.)

(a) Beta decay is nuclear decay in which an electron is emitted. If the electron is given 0.750 MeV of kinetic energy, what is its velocity? (b) Comment on how the high velocity is consistent with the kinetic energy as it compares to the rest mass energy of the electron.

A spaceship, 200 m long as. seen on board, moves by the Earth at 0.970c. What is its length as measured by an earthbound observer?

Calculate the momentum of a proton moving with a speed of (a) 0.010c, (b) 0.50c, (c) 0.90c. (d) Convert the answers of (a)(c) to MeV/c.