7. The Lagrangian of a particle of mass m moving in one dimension is given by: L= m -bx Where b is a positive constant. The coordinate of the particle x (t) at a time t is given by: A. - t? + C, t+ C2 B. C, t + C2 c. C, Cos () + C, Sin () D. C, Cosh () + Sinh ()
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- H2. Suppose a particle of constant mass m with position x > 0, moves in one space dimension under the influence of the gravitational force of another point particle of constant mass M sitting at x = 0, i.e. the attracting force is F: (a) Using Newton's second law, show that d -mx². dt GmM x² i. GmM X = 0. dv dv (i.e., the total energy, sum of kinetic and potential energy, is conserved). (b) Using the change of variables var dr, solve the equation of motion and determine the = dx velocity of the particle v(x) as a function of x assuming it starts with zero velocity at xo. Does the particle's speed in x O depend on the initial position? dt' =Qno7 solve asap. Physics expert plz suggest4 Part A At what speed, as a fraction of c, will a moving rod have a length 60% that of an identical rod at rest? v = ΜΕ ΑΣΦ ? C
- Peggy, standing on a moving railroad car, passes Ryan at velocity ν. Peggy and Ryan both measure the length of the car, from one end to theother. The length Peggy measures is _______ the length Ryan measures.A. Longer than B. The same as C. Shorter than1. Two atomic clocks are synchronized. One is placed on a satellite, which orbits around the earth at high speed for a whole year. The other is placed in a lab and remains at rest, with respect to the earth. You may assume that both clocks can measure time accurately to many significant digits. a. Will the two clocks still be synchronized after one year? Explain your reasoning. b. Imagine that the speed of light was much slower than its actual value. How would the results of this experiment change if the speed of light was only twice the average speed of the satellite? Explain your reasoning, using a calculation.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?
- q3What is the total energy of an electron moving with a speed of 0.950 c? a. 2.6 x 10-13 J b. 1.1 × 10-13J c. 1.2 x 10-14 J d. 8.2 × 10-14 JA 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--- v