SSM (a) A neutron of mass mn and kinetic energy K makes a head-on elastic collision with a stationary
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- to Eni Consider a system that consists of N noninteracting particles in a cubical container of edge length L. Assuming that the force exerted by the ith particle in a collision with a wall δε perpendicular the x-direction is given by where 2 π²ħ² n² ny n iy IZ + + 2mL LL₂ m² = 3 (n²x + n², + n/² ) ₂2), prove that F 2 2 ix 2 Miy iz ix ix prove that pressure P = 2N i = 1,2,..., N 3V E = 28, n; 3L Fix = - (a) n₁ aLx If _L₂ = L₁ = L₂ = L and (b) If the average force is defined as F = N(F₁x), ). (c) From the result of (b), derive that the system obeys the ideal gas law PV = Nk„T (hint: you can apply the equipartition of energy theorem for (s)). niarrow_forwardPls help ASAP on both pls i begarrow_forwarda) A proton (p) of mass 1.43-u(unified atomic mass units) traveling with a speed 4.13 x 104 m/s of has an elastic head-on collision with a helium (He) nucleus (mHe = 4.00 u) initially at rest. What is the velocity of helium nucleus after the collision? (As mentioned in Chapter 1, 1 u = 1.66 x 10–27 kg but we won’t need this fact.) Assume the collision takes place in nearly empty space. b) A proton (p) of mass 2.48-u(unified atomic mass units) traveling with a speed 2.64 x 104 m/s of has an elastic head-on collision with a helium (He) nucleus (mHe = 4.00 u) initially at rest. What is the velocity of helium nucleus after the collision? (As mentioned in Chapter 1, 1 u = 1.66 x 10–27 kg but we won’t need this fact.) Assume the collision takes place in nearly empty space.arrow_forward
- In a dark matter direct detection experiment, a dark matter particle is supposed to directly interact with the atoms in the detector, causing either a nucleus or an electron to recoil after the collision has occurred. The dark matter particles in our galaxy should be moving at non-relativistic speeds, so this scattering process can be described using the conservation of momentum governed by Newton's laws without the need for quantum mechanics. One of the most common target materials for these experiments is xenon. Your goal is to answer the following question. Assuming there is a dark matter particle with incident velocity v1 that will scatter from a Xe-136 nucleus (with a mass of 136 amu) that was initially at rest as shown below. What is the dark matter mass? You should solve for the answer symbolically first. Then you will substitute in the values shown below to get out an actual numerical value for the mass, in amu. Dark Matter Particle 02 01 Өз Xe nucleusarrow_forwardTwo 2.9 kg bodies, A and B, collide. The velocities before the collision are v→A=(45î+22ĵ)m/s and v→B=(31î+5.7ĵ)m/s. After the collision, v→A′=(12î+13ĵ)m/s. What are (a) the x-component and (b) the y-component of the final velocity of B? (c) What is the change in the total kinetic energy (including sign)? (a) Number Enter your answer for part (a) in accordance to the question statement Units Choose the answer for part (a) from the menu in accordance to the question statement This answer has no units° (degrees)mkgsm/sm/s^2NJWN/mkg·m/s or N·sN/m^2 or Pakg/m^3gm/s^3times (b) Number Enter your answer for part (b) in accordance to the question statement Units Choose the answer for part (b) from the menu in accordance to the question statement This answer has no units° (degrees)mkgsm/sm/s^2NJWN/mkg·m/s or N·sN/m^2 or Pakg/m^3gm/s^3times (c) Number…arrow_forward(a) If the system's kinetic energy, as measured from the Earth reference frame, decreases by 20% because of the collision, what are the final velocities of the balls? (b) What change in internal energy has occurred? (c) An observer watches this collision from a reference frame moving at a velocity of 15 m/ s to the east relative to the Earth reference frame. What changes in kinetic energy does this observer measure?arrow_forward
- A bullet of mass m = 10 g and speed vo = 540 m/s is fired at a stationary block of mass M= 200 g. The bullet bounces straight backward with half of its initial speed (v' = 0.5vo). Assume friction between the block and the surface is negligible. (a) Determine the speed of the block just after the collision. (b) Is the collision elastic? Why? (c) How much the momentum of the block has changed? (AP block) (d) If collision lasts for 20 us (At = 20×10-6 s), determine magnitude of the average force (Fave.) exerted on the block by the bullet. Vo (e) Now, suppose the bullet has the speed of vo = 540 m/s before collision and bounces straight backward with half of its initial speed (v' = 0.5vo) but the block splits into two pieces. The figure below shows a top view of the collision. If one piece with mass mį = 80 g goes off with a speed of vi = 25 m/s at 01 = 37°. At what direction and speed does the other piece travel? (v, and 02) 37°arrow_forwardA proton that has a mass m and is moving @ 400m/s in the +i direction undergoes a head-on elastic collision with a stationary oxygen nucleus of mass 16m. Find the velocities of the proton and the oxygen nucleaus after the collision.arrow_forwardAs shown in the figure below, a bullet is fired at and passes through a piece of target paper suspended by a massless string. The bullet has a mass m, a speed v before the collision with the target, and a speed (0.516)v after passing through the target. (a) Before collision M V m PHAC The collision is inelastic and during the collision, the amount of energy lost is equal to fraction [(0.423)KE BC] of the kinetic energy of the bullet before the collision. Determine the mass M of the target and the speed V of the target the instant after the collision in terms of the mass m of the bullet and speed v of the bullet before the collision. (Express your answers to at least 3 decimals.) V = M = M (b) After collisionarrow_forward
- As shown in the figure below, a bullet is fired at and passes through a piece of target paper suspended by a massless string. The bullet has a mass m, a speed v before the collision with the target, and a speed (0.506)v after passing through the target. The collision is inelastic and during the collision, the amount of energy lost is equal to a fraction [(0.443)KEb BC] of the kinetic energy of the bullet before the collision. Determine the mass M of the target and the speed V of the target the instant after the collision in terms of the mass m of the bullet and speed v of the bullet before the collision. (Express your answers to at least 3 decimals.) V = vM = marrow_forwardAs shown in the figure below, a bullet is fired at and passes through a piece of target paper suspended by a massless string. The bullet has a mass m, a speed v before the collision with the target, and a speed (0.506)v after passing through the target. The collision is inelastic and during the collision, the amount of energy lost is equal to a fraction [(0.443)KEb Bc) of the kinetic energy of the bullet before the collision. Determine the mass Mof the target and the speed Vof the target the instant after the collision in terms of the mass mof the bullet and speed vof the bullet before the collision. (Express your answers to at least 3 decimals.) V= vM= m M M (a) Before collision (b) After collisionarrow_forwardA particle with mass mA is struck head-on by another particle with mass mB that isinitially moving at speed v0 . The collision is elastic.(a) What percentage of the original energy does each particle have after the collision?(b) For what values, if any, of the mass ratio mA /mB is the original kinetic energy sharedequally by the two particles after the collision?arrow_forward
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning