# Energy and Momentum Problems ```Accelerated Physics Energy and Momentum Problems
Name ______________________________________ Date _________ Hr. ___
Formulas
Momentum
p = mv
Ft = 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 cos1 + m2v2f cos2
0 = m1v1f sin1 + m2v2f sin2
Energy
W = Fav d cos
W = PE + KE + WNC
KE = 1/2mv2
PEgrav = mgh
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.
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