you have been hired as an expert witness for an attorney who is representing a speeding driver

Problem 1

In a laboratory frame of reference, an observer notes that Newton's second law is valid. Assume forces and masses are measured to be the same in any reference frame for speeds small compared with the speed oflight.

Problem 2

A car of mass 2000 k g moving with a speed of 20.0 m / s collides and locks together with a 1500 -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.

Problem 3

A meterstick moving at 0.900 c relative to the Earth's surface approaches an observer at rest with respect to the Earth's surface. (a) What is the meterstick's length as measured by the observer? (b) Qualitatively, how would the answer to part (a) change if the observer started running toward the meterstick?

Problem 4

A muon formed high in the Earth's atmosphere is measured by an observer on the Earth's surface to travel at speed v = 0.990 c for a distance of 4.60 k m before it decays into an electron, a neutrino, and an antineutrino ( μ − → e − + ν + ν ¯)#N#(a) For what time interval 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?.

Problem 5

A deep-space vehicle moves away from the Earth with a speed of 0.800 c. An astronaut on the vehicle measures a time interval of 3.00 s to rotate her body through 1.00 rev as she floats in the vehicle. What time interval is required for this rotation according to an observer on the Earth?

Problem 6

An astronaut is traveling in a space vehicle moving at 0.500 c 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 the Earth when the vehicle is moving in a direction perpendicular to the line that connects the vehicle with an observer on the Earth.

Problem 7

For what value of v does γ = 1.0100 ? Observe that for speeds lower than this value, time dilation and length contraction are effects amounting to less than 1 %.