Exam 39: Relativity

A 1000-kg automobile moving with a speed of 24 m/s relative to the road collides with a 500-kg automobile initially at rest. If the two stick together, what is the velocity in m/s of the two cars after the collision according to an observer in a truck moving 10 m/s in the same direction as the moving cars?

Hanna, at rest in her spaceship which is moving past Earth at 0.800 c, observes a neutron at rest relative to her spaceship decay into a proton, an electron and a neutrino. She notes that the total momentum, , of the decay products is zero after the decay. According to an observer on Earth, the magnitude of the total momentum of the decay products, , is

When 1.0 gram of hydrogen combines with 8.0 grams of oxygen, 9.0 grams of water is formed. But is this true? During the reaction 2.86 × 10⁵ J of energy is released. How much mass is actually lost in this reaction?

A boat has an initial velocity of 2 m/s in the y direction on a stream which is moving in the x direction at 1 m/s. The boat is accelerating in its direction of motion at 1 m/s². What is the acceleration of the boat (in m/s²) relative to the water?

The period of a pendulum is 2.0 s in a stationary inertial frame of reference. What is its period when measured by an observer moving at a speed of 0.60 c with respect to the inertial frame of reference?

A jet plane travels around the world at 2 000 mi/hr (894 m/s). Two accurate atomic clocks measure the times of flight, one on board the plane and the second on Earth. If it takes 12 hours to complete the journey, what will the time difference (in μs) be?

The first intergalactic spaceship is headed toward the Magellanic Clouds at a speed of 0.8c. The spaceship is 1 000 m long. Clocks at the front and the rear of the spaceship both read 3:00 P.M. Can it be 3:00 P.M. simultaneously at the front and the back of the spaceship?

Two spaceships traveling in opposite directions along parallel lines measure their own and the other spaceship's length while passing one another. The crew on spaceship A says that their ship is 1000 m long and that ship B is 800 m long. The crew on ship B says that their ship is 1000 m long and that ship A is 800 m long. At what speed does each crew say that the other ship is traveling relative to their own ship?

In a classroom on the first spaceship to an extrasolar planet--there are children because the trip will take 200 years--a teacher is showing charge Q uniformly distributed along a conducting rod of length L₀ to produce linear charge density λ₀. As observed on Pluto when the spaceship passes it at 0.800 c, the linear charge density is

The quantity which does not change in magnitude from that observed in system S when observed in system S' moving away from system S at speed v is

Energy is released during a nuclear reaction due to a conversion between mass and energy. Mass is not conserved. The initial and final amounts are different. If a total of 1.0 gram of mass is "missing", how much energy has been released?

The half-life of a muon is 2.20 μs as measured in a stationary reference frame. What is the half life of the muon (in μs) when it is moving with a speed of v = 0.800 c?

The 500 m-long spaceship Springbrake is at rest on the planet Hitest for refueling. Another spaceship, Summerbrake, passes parallel to Springbrake at 0.600c. The crew on Springbrake measure the length of Summerbrake as it passes and find that the length they measure is exactly the same as the known 500 m rest length of Springbrake. If Summerbrake were at rest next to Springbrake, its length would then be measured to be

Assume a gram of a substance marketed as "Pure Energy" is annihilated by a gram of a second substance "Anti-Pure Energy." How long would the energy released power a city which uses 10⁹ watts of power?