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Accelerated Physics Energy and Momentum Problems Name ______________________________________ Date _________ Hr. ___ Formulas Momentum p = mv Ft = p = m(vf –vI) m1vi1 + m2vi2 = m1vf1 + m2vf2 m1vi1 + m2vi2 = (m1 + m2) vf vif = (m1 - m2) v1i + 2m2 v2i (m1 + m2) (m1 + m2) (Elastic one dimension collisions) v2f = 2m1 v1i + (m2 - m1) v2i (m1 + m2) (m1 + m2) m1v1I = m1v1f cos1 + m2v2f cos2 0 = m1v1f sin1 + m2v2f sin2 Energy W = Fav d cos W = PE + KE + WNC KE = 1/2mv2 PEgrav = mgh Fa = kx PEspring = 1/2 k x2 PEi + KEi = PEf + KEf + WNC PE + KE = W NC P = W/t = Fav v (Two dimension collision) - target initially at rest 1HP = 746W 1/2m1v1i2 + 1/2m2v2i2 = 1/2m1v1f2 + 1/2m2v2f2 vi1 - vi2 = - (vf1 - vf2) (horizontal –elastic collision) Practice Problems 1. A radioactive nucleus at rest decays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and have momenta of 9.3x10-23 kgm/s and 5.4x10-23 kgm/s, respectively. What is the magnitude and direction of the momentum of the second (recoiling) nucleus? (Hint: momentum vectors) 2. Two billiard balls of equal mass undergo a perfectly elastic head-on collision. If the speed of one ball is 2m/s, and the other 3m/s in the opposite direction, what will their speeds be after the collision? 3. A proton traveling with speed 8.2 x 105 m/s collides elastically with a stationary proton in a hydrogen target. One of the protons is observed to be scattered at a 60 0 angle. At what angle will the second proton be observed, and what will be the velocities of the two protons after the collision? 4. An 18g riffle bullet travelling 200m/s buries itself in a 3.6kg pendulum hanging on a 2.8m long string, which makes the pendulum swing upwards in an arc. a) Use conservation of momentum to determine the velocity of the pendulum (and bullet) after it is hit and b) use conservation of energy to determine the maximum height of the pendulum above its rest position.