A particle of mass 'm' is moving in a potential V(x) = -ax² + bx4 . Find the time period and frequency of the mass.
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- The muon is an unstable subatomic particle witha mean lifetime of 2.2 μs, and about 10,000 muons reach everysquare meter of the earth's surface a minute. A muon has a linear momentum G, and after some short time it decays into two other elementary particles with masses m1 and m2. The energy Q released during the decay is converted entirely into the kinetic energy of the decay products (i.e., into kinetic energy of m1 and m2). Find linear momenta of decay products. Draw a vector diagram showing a range of momenta decay products can take.The space and time coordinates for two events as measured in a frame S are as follows: Event 1: x1=x0 , t1=x0/c Event 2: x2=2x0, t2=x0/2c a. There exists a frame in which these events occur at the same time. Find the velocity of this frame with respect to S. b. What is the value of t at which both events occur in the new frame?The lifetime of a free neutron is 886 s. If a neutron moves with a speed of 2.57 ✕ 108 m/s relative to an observer in the lab, what does the observer measure the neutron's lifetime to be (in s)?
- The time interval ΔΔt between two events measured by an observer moving with respect to a clock1 is usually shorter than the time interval ΔΔtp (ΔΔt < ΔΔtp) between the same two events measured by an observer at rest with respect to the clock. Group of answer choices True FalseThe muon is an unstable particle that spontaneously decays into an electron and two neutrinos. In a reference frame in which the muons are stationary, if the number of muons at t = 0 is N0, the number at time t is given by , where τ is the mean lifetime, equal to 2.2 ms. Suppose the muons move at a speed of 0.95 c and there are 5.0 × 104 muons at t = 0. (a) What is the observed lifetime of the muons? (b) How many muons remain after traveling a distance of 3.0 km?A particle has a rest energy of 4.31×10−13 J and a total energy of 8.33×10−13 J. Calculate the momentum p of the particle.
- A train, which is 200 m long, approaches a tunnel, which is 120 m long. The train is moving at a velocity of 0.89 c. a. What is the length of the train as seen be someone standing at the entrance to the tunnel? m b. Is the train ever entirely inside the tunnel as seen be the observer at the entrance to the tunnel? ONLY 1 ATTEMPT IS ALLOWED FOR THIS PART. ---Select--- v c. What is the length of the tunnel as seen be a passenger on the train? m d. Is the train ever entirely inside the tunnel as seen by the passenger on the train? ONLY 1 ATTEMPT IS ALLOWED FOR THIS PART. ---Select--- vEvents 1 and 2 are exploding firecrackers that each emit light pulses. In the reference frame of the detector, event 1 leaves a char mark at a distance 3.40 m from the detector, and event 2 leaves a similar mark at a distance 2.10 m from the detector. If the two events are simultaneous in the reference frame of the detector and occur at instant t = 0, at what instant of time will each light pulse be detected?