A constant force Facting on a particle of mass m changes the velocity from ₁ to ₂ in time T. (a) Prove that ♬ = m(v₂ − ₁)/π (b) Does the result in (a) hold if the v₂ force is variable? Explain.
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- An electron has a momentum of 2.00 x 10-2¹ kg⋅m/s. Find the kinetic energy of the electron in units of MeV. (A) 2.31 (B) 5.74 (C) 4.97 (D) 3.27 (E) 6.49Two manned satellites approaching one another, at a relative speed of 0.200 m/s, intending to dock. The first has a mass of 5.00 ✕ 103 kg, and the second a mass of 7.50 ✕ 103 kg. a. Calculate the final velocity (after docking) in m/s by using the frame of reference in which the first satellite was originally at rest. (Assume the second satellite moves in the positive direction. Include the sign of the value in your answer.) m/s b. What is the loss of kinetic energy (in J) in this inelastic collision? J c. Repeat both parts by using the frame of reference in which the second satellite was originally at rest. final velocity (m/s) m/sloss of kinetic energy (J) J Explain why the change in velocity is different in the two frames, whereas the change in kinetic energy is the same in both.An object is made of glass and has the shape of a cube 0.11 m on a side, according to an observer at rest relative to it. However, an observer moving at high speed parallel to one of the object's edges and knowing that the object's mass is 3.6 kg determines its density to be 8700 kg/m3, which is much greater than the density of glass. What is the moving observer's speed (in units of c) relative to the cube?
- Find the velocity (in m/s) of a proton that has a momentum of 3.88 ✕ 10−19 kg · m/s.There are two relativistic particles of identical mass m that move towards each other along the same axis. The magnitudes of their momenta are the same. They collide head-on to form a new particle of mass 8m. What were the magnitudes of momenta of the initial particles?Suppose two particles are traveling along the space curves r1(t)=< t2,, 8t-16, t2 > and r1(t)=< 3t+4, t2, 5t-4, >. A collision will occur when the two particles arrive at the same point at the same time. Find any time(s) and location(s) when and where the particles collide
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- (b) A particle of unit mass moving in one dimension obeys the equation of motion x = (i) Show that i2 – e" is a constant of the motion. (ii) At t = 0 the particle is at x = 0 and at rest, i.e. x(0) = ¿(0) = 0. Show that the particle reaches x = +o at finite t > 0. Hint: use the result of part (i) to write the time taken to reach x = +0 as an integral. (iii) What is a suitable Lagrangian for this system?A particle of mass M, which was initially at rest, is hit by a particle of mass m, which is travelling at the speed Vi. The two particles collide and travel in different directions at the same pace Vf. Find the mass ratio M/m in terms of ß = vi/c, assuming a relativistic, elastic collision. Demonstrate that this reduces to Vi 0, the nonrelativistic meaning.