Problem 1
(5 pts)
A bullet of mass
m=
38 g is fired horizontally and at a distance
d=
5 cm above the axis of
a cylinder of mass
M=
10 kg, radius
R=
11 cm and length
L=
20 cm. The cylinder is
initially at rest and is free to rotate on a massless axle through it's long axis. The bullet
adheres to the cylinder surface as it hits it. The cylinder begins to rotate at an angular
speed such that it completes one complete revolution in
T=
0.211 s after catching the
bullet. Calculate the initial speed of the bullet prior to impact. (The moment of intertia of
a cylinder is
2
1
2
I
MR
=
)
A. 955
m/s
B. 1910
m/s
C. 1105
m/s
D. 865
m/s
E. 745
m/s
Problem 2 (5 pts)
Particle 1 of mass
m
moving with speed
v
in the +x direction has an elastic collision with
particle 2 of mass 3
m
which was originally at rest. After the collision, particle 2 is
moving in the +x direction. What is its speed?
A.
2
5
v
B.
1
3
v
C.
2
3
v
D.
1
2
v
E.
2
7
v
Problem 3 (5 pts)
The first excited state of a particular atom in a gas is
5.2
eV above the ground state. A
moving electron collides with one of these atoms, and excites the atom to its first excited
state. Immediately after the collision the kinetic energy of the electron is
2
eV. What was
the kinetic energy of the electron just before the collision?
A) 7.2 eV
B) 3.2 eV
C) 2.6 eV
D) 10.4 eV
E) 1.6 eV
Problem 4 (5 pts)
Consider a system consisting of three particles:
m
1
= 2 kg,
1
= < 8, -8, 14 > m/s
m
2
= 3 kg,
2
= < -15, 7, -4 > m/s
m
3
= 3 kg,
3
= < -28, 39, 23 > m/s
What is the velocity of the center of mass of this system?
A) <-14.1, 15.3, 10.6> m/s
B) <-8.2, 21.2, 13.6> m/s
C) <-12.2, 10.3, 10.6> m/s
D) <14.4, -14.9, 13.6> m/s
E) <-15, 15.4, 11,6> m/s