A particle of mass m is moving with speed 2v and collides with a mass 2m moving with speed v in the same direction. After collision, the first mass is stopped completely while the second one splits into two particles each of mass m, which move at angle 45° with respect to the original direction. The speed of each of the moving particle will be (a) √√2 v (d) 2√2 v (b) √22 (c) V (2√2)
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- A moving hydrogen atom (rest mass = 939 MeV/c2, where c is the speed of light in vacuum) has a kinetic energy of 313 MeV. (a) What is the total energy of this atom in MeV? (b) What is this particle's speed in terms of c? (c) What is the magnitude of this atom's linear momentum?A block of mass m= 2 kg is moving with speed 7ms^-1. It collides inelastically with a stationary block of unknown mass M. The two move off with velocity 5 ms^-1. What’s the value of M?Two particles each of mass m are traveling toward each other with equal speeds v in reference frame O. They collide and form a new composite particle of mass M. (a) Is the mass M greater than 2m, equal to 2m, or less than 2m? (b) Observer O ′ is in motion relative to O with speed v in the same direction as one of the particles, so that particle appears to be at rest in O ′. Will O ′ agree with the answer to question (a)?
- An object is made of glass and has the shape of a cube 0.10 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 2.7 kg determines its density to be 7500 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? Number i w 40- Rest frame of cube Units + KL 20 Rest frame of observerAn unstable particle is at rest and suddenly breaks up into two fragments. No external forces act on the particle or its fragments. One of the fragments has a velocity of +0.704c and a mass of 2.26 × 10-27 kg, and the other has a mass of 4.88 × 10-27 kg. What is the velocity of the more massive fragment (as a multiple of c)? (Hint: This problem is similar to Example 6 in Chapter 7.) Number i -1.25E8 V2 m2 C hr Unstable particle at rest Units ✔ breaths/min km kg/s ing fragmentsA spacecraft has a nonrelativistic (or classical) momentum whose magnitude is 1.4 × 10¹3 kg-m/s. The spacecraft moves at such a speed that the pilot measures the proper time interval between two events to be one half the dilated time interval. Find the relativistic momentum of the spacecraft. Prel=
- Electromagnetic radiation from a star is observed with an earth-based telescope. The star is moving away from the earth with a speed of 0.580c. If the radiation has a frequency of 8.64 x 1014 Hz in the rest frame of the star, what is the frequency measured by an observer on earth?Some particles are created via collisions. For instance, pions are created via collisions with high energy protons and carbon, which releases neutrons and pions (which they themself, decay into muons). Suppose two particles with momenta of pi = (2, -1,0,0) kg and p2 = (4,1, 1,0) kg collide. Three particles are created as a result from this collision, two of which have momenta of P3 = (1,0.5, 0, 0) kg and p4 = (1, -1,0,0) kg, determine the four momentum, energy, rest mass and three velocity of the third daughter particle. %3DAn object is made of glass and has the shape of a cube 0.12 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 3.4 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? Rest frame of cube KL-Lo Rest frame of observer
- Starting from rest, two skaters "push off" against each other on smooth level ice, where friction is negligible. One is a woman and one is a man. The woman moves away with a velocity of +2.0 m/s relative to the ice. The mass of the woman is 57 kg, and the mass of the man is 76 kg. Assuming that the speed of light is 3.5 m/s, so that the relativistic momentum must be used, find the recoil velocity of the man relative to the ice. (Hint: This problem is similar to Example 6 in Chapter 7.) Number i UnitsStarting from rest, two skaters "push off" against each other on smooth level ice, where friction is negligible. One is a woman and one is a man. The woman moves away with a velocity of +2.2 m/s relative to the ice. The mass of the woman is 57 kg, and the mass of the man is 88 kg. Assuming that the speed of light is 2.8 m/s, so that the relativistic momentum must be used, find the recoil velocity of the man relative to the ice. (Hint: This problem is similar to Example 6 in Chapter 7.) Number i UnitsA particle of mass m moves with a momentum of magnitude p. Show that the kinetic energy of the particle KE = p2/2m