FIGURE Q36.1 shows two balls. What are the speed and direction of each (a) in a reference frame that moves with ball 1 and (b) in a reference frame that moves with ball 2?

FIGURE Q36.1

Teenagers Sam and Tom are playing chicken in their rockets. As FIGURE Q36.2 shows, an experimenter on earth sees that each is traveling at 0.95c as he approaches the other. Sam fires a laser beam toward Tom.

FIGURE Q36.2

1. What is the speed of the laser beam relative to Sam?

2. What is the speed of the laser beam relative to Tom?

Firecracker A is 300 m from you. Firecracker B is 600 m from you in the same direction. You see both explode at the same time. Define event 1 to be “firecracker A explodes” and event 2 to be “firecracker B explodes.” Does event 1 occur before, after, or at the same time as event 2? Explain.

Firecrackers A and B are 600 m apart. You are standing exactly halfway between them. Your lab partner is 300 m on the other side of firecracker A. You see two flashes of light, from the two explosions, at exactly the same instant of time. Define event 1 to be “firecracker A explodes” and event 2 to be “firecracker B explodes.” According to your lab partner, based on measurements he or she makes, does event 1 occur before, after, or at the same time as event 2? Explain.

FIGURE Q36.5 shows Priya standing at the center of her railroad car as it passes Ryan on the ground. Firecrackers attached to the ends of the car explode. A short time later, the flashes from the two explosions arrive at Priya at the same time.

FIGURE Q36.5

1. Were the explosions simultaneous in Priya’s reference frame? If not, which exploded first? Explain.

2. Were the explosions simultaneous in Ryan’s reference frame? If not, which exploded first? Explain.

FIGURE Q36.6 shows a rocket traveling from left to right. At the instant it is halfway between two trees, lightning simultaneously (in the rocket’s frame) hits both trees.

FIGURE Q36.6

1. Do the light flashes reach the rocket pilot simultaneously? If not, which reaches her first? Explain.

2. A student was sitting on the ground halfway between the trees as the rocket passed overhead. According to the student, were the lightning strikes simultaneous? If not, which tree was hit first? Explain.

Your friend flies from Los Angeles to New York. She carries an accurate stopwatch with her to measure the flight time. You and your assistants on the ground also measure the flight time.

1. Identify the two events associated with this measurement.

2. Who, if anyone, measures the proper time?

3. Who, if anyone, measures the shorter flight time?

As the meter stick in FIGURE Q36.8 flies past you, you simultaneously measure the positions of both ends and determine that $L<1\text{m}$.

FIGURE Q36.8

1. To an experimenter in frame $\text{S}\prime$, the meter stick’s frame, did you make your two measurements simultaneously? If not, which end did you measure first? Explain.

2. Can experimenters in frame $\text{S}\prime$ give an explanation for why your measurement is less than 1 m?

A 100-m-long train is heading for an 80-m-long tunnel. If the train moves sufficiently fast, is it possible, according to experimenters on the ground, for the entire train to be inside the tunnel at one instant of time? Explain.

Particle A has half the mass and twice the speed of particle B. Is the momentum $p_{\text{A}}$ less than, greater than, or equal to $p_{\text{B}}?$ Explain.

Event A occurs at spacetime coordinates $(300\text{m,}2\mu \text{s})$.

1. Event B occurs at spacetime coordinates $(1200\text{m,}6\mu \text{s})$. Could A possibly be the cause of B? Explain.

2. Event C occurs at spacetime coordinates $(2400\text{m,}8\mu \text{s})$. Could A possibly be the cause of C? Explain.