3rd Common Quiz (empty)

Physics 111 Honors Common Exam 3 Fall 2002
Name: Section:
Closed book exam. Only one 8.5 ′′ × 11 ′′ formula sheet (front and back side) can be used. Calculators are
allowed. Use the scantron forms (pencil only!) for the multiple choice problems. Circle the answers on the
examination sheet as well, and return it together with the scantron form. Use the back of these pages, or
attach your own pages with solutions for problems which require calculations.
The multiple-choice problems are 5 points each. Partial credit (up to 3 points) will be given for multiplechoice
problems, if you provide a detailed solution on the examination sheets. The work-out problems are
10 points each. Up to 5 points of extra credit will be given for a clear and legible presentation of your
results. The nominal number of points is 100.
Clearly print your first and last name and indicate your section number on both the scantron form and the
examination sheet.
Multiple-Choice Problems
Good luck!
Problem 1: A roller coaster has a mass of m = 1120 kg when fully loaded with passengers. As the car
passes over the top of a circular hill of radius r = 15 m, its speed is not changing. What is the magnitude
and direction of the force of the track on the car at the top of the hill if the car’s speed is 12 m/s?
A) 235 N (up)
B) 235 N (down)
C) 0 N
D) 21.7 kN (up)
E) 21.7 kN (down)
Problem 2: A 40.0 kg child standing on a frozen pond throws a 0.675 kg stone to the east with a speed of
4.33 m/s. Neglecting friction between the child and ice, find the recoil velocity of the child!
A) 1.69 cm/s
B) 7.31 cm/s
C) 10.8 cm/s
D) 5.00 m/s
E) 7.31 m/s

Problem 3: A disk of radius R has been stamped out (removed) from a uniform metal plate P of radius 2R.
Using the xy-coordinate system shown, locate the center of mass (xp,yp) of the plate.
A) (xp = 0,yp = 0)
B) (xp = 0,yp = 1 4 R)
C) (xp = 1 4 R,yp = 0)
D) (xp = 1 3 R,yp = 0)
E) (xp = 2 5 R,yp = 0)
Problem 4: Three thin rods, each of length L, are arranged in an inverted U. The two rods on the arm of
the U have mass M and the third rod has the mass 3M. Where is the center of mass of the assembly for the
vertical component ycom as measured from the third rod.
A) ycom = 1 5 L
B) ycom = 2 5 L
C) ycom = 3 5 L
D) ycom = 1 3 L
E) ycom = 2 3 L
Problem 5: A pitched 140 g baseball, in horizontal flight with a speed vi = 42.0 m/s, is struck by a bat.
After leaving the bat, the ball travels in opposite direction with a speed, also v f = 42.0 m/s. If the average
force during the impact is Favg = 10.0 kN, what is impact time Δt for the baseball/bat collision?
A) 0.588 ms
B) 1.18 ms
C) 4.20 ms
D) 8.40 ms
E) 10.0 ms

Problem 6: A bullet (mb = 9.78 g) is fired into a stationary block of wood (mw = 4.52 kg), coming quickly
to rest inside the block. The speed of the bullet/wood combination after the collision is 0.512 m/s. What
was the original speed of the bullet?
A) 11 m/s
B) 121 m/s
C) 237 m/s
D) 335 m/s
E) 463 m/s
Problem 7: A steel ball of mass 0.436 kg is fastened to a cord that is 0.875 m long and fixed at the far end.
The ball is then released when the cord is horizontal. At the bottom of the path, the ball strikes a 3.25 kg
steel block initially at rest on a frictionless surface. The collision is elastic. Find the speed of the block after
the collision!
A) 0.490 m/s
B) 0.693 m/s
C) 0.980 m/s
D) 1.11 m/s
E) 7.31 m/s
Problem 8: Which of the following statements is false?
A) A collision is an isolated event in which two or more bodies (the colliding bodies) exert relatively
strong forces on each other for a relatively short time.
B) In a closed isolated system containing a collision, the linear momentum of each colliding body may
change but the total linear momentum P of the system cannot change, whether the collision is elastic
or inelastic.
C) If no net external force acts on a system of particles, the total linear momentum P of the system
cannot change.
D) In an elastic collision, the kinetic energy of each colliding body may change, but the total kinetic
energy of the system does not change.
E) The linear momentum P of a system of particles is equal to the product of the total mass M and the
acceleration of the center of mass acom.

Problem 9: A rigid sculpture consists of a thin hoop of mass mhoop = 1.25 kg and radius Rhoop = 0.15 m
and a thin radial rod of mass mrod = 0.68 kg and length Lrod = 2Rhoop. The sculpture can pivot around a
horizontal axis in the plane of the hoop passing through its center. What is the sculptures rotational inertia
I about the rotation axis?
A) 2.8 × 10 −1 kg m 2
B) 5.3 × 10 −1 kg m 2
C) 1.5 × 10 −2 kg m 2
D) 4.1 × 10 −2 kg m 2
E) 8.0 × 10 −2 kg m 2
Problem 10: A cylinder having a mass of 3.5 kg can rotate about its central axis through point O Four
forces are applied as shown: F1 = 4.5 N, F2 = 3.4 N, F3 = 1.7 N, and F4 = 4.9 N. The radial distances are
R1 = 13 cm and R2 = 28 cm, respectively. Find the magnitude and direction of the angular acceleration of
the cylinder.
A) 0.087 rad/s 2 (clockwise)
B) 0.63 rad/s 2 (clockwise)
C) 0 rad/s 2
D) 0.63 rad/s 2 (counter-clockwise)
E) 0.087 rad/s 2 (counter-clockwise)

Work-Out Problems
Please indicate your final answers and make sure that all the steps of your solution are shown!
Problem A: Two cars with the same mass are involved in an accident. Car A was travelling East and car
B South before the collision. Assume that the accident is an inelastic collision. In what direction, will the
wreckage of the cars move after the collision, if the initial speed of car A is 2.24 times that of car B?
Problem B: A proton of mass 1.0 u moving in the positive x-direction with an initial velocity vpix collides
elastically with an α-particle of mass 4.0 u that is initially at rest. After the collision, the proton moves in
the negative y-direction.
a) Provide a sketch!
b) What is the speed of the proton after the collision vp f y in terms of vpix?
c) What is the speed of the α-particle after the collision vα f in terms of vpix?
d) What is the angle θ between proton and α-particle after the collision?

Problem C: Ramon Unzaga, from Spain, is credited to have performed the first bicycle kick in 1914, and
Pelé made it world famous in the 60s and 70s. The figure shows an analysis of a Pelé’s bicycle kick. Main
phases of the bicycle kick: the jumping (1), the scissors (2), and the ball striking (3). (a) Vertical position
of the center of gravity CG of the whole body and (b) only of the trunk. (c) Angular position of the legs.
(d) Rotational inertia of the kicking leg. (e) The angular momentum of the whole body and of each leg.
a) How long does it take to perform the bicycle
kick?
b) How long is the soccer player in the air?
c) What are the laws of physics that describe the
position of the center of mass?
d) The angular momentum L = Iω of the whole
body is almost constant during the aerial phase.
How does the soccer player achieve an effective
kick so that the ball obtains a high velocity?
e) When is the inertia of the kicking leg a minimum?
What does that mean for the angular
acceleration and the kinetic energy associated
with the rotation?
f) Is the angular momentum conserved during the
kick?

Problem D: If Icom is the rotational inertia of a body about a parallel axis that extends through the body’s
center of mass, and h is the perpendicular distance between the given axis and the axis through the center
of mass, then the rotational inertia I about the given axis is
I = Icom + Mh 2 ,
where M is the total mass of the body. This equation is known as the Parallel-Axis Theorem. Please show
the proof of the parallel-axis theorem! Provide a clear sketch in an appropriate coordinate system, clearly
indicate all your variables, and explain every step of the proof.
Problem E: Some modern hybrid cars use a flywheel to store kinetic energy. The car has a mass of 1500 kg
and decelerates from 40 km/h to a full stop in 4.5 s. The flywheel consists of an annular cylinder of mass
33.0 kg with inner radius r1 = 0.1 m and outer radius r2 = 0.2 m.
a) What is the initial kinetic energy of the car?
b) What is the rotational inertia of the flywheel?
c) Assume that the kinetic energy is conserved during the deceleration, what is the angular velocity of
the flywheels rotation in revolution per second?
d) What is the angular acceleration of the flywheel during the deceleration of the car in revolutions per
second 2 ? (Assume that the angular acceleration is constant and that the flywheel was not rotating
when the car started to break).
Before you turn in your quiz, please double-check you multiple-choice answers. Are they marked
correctly on the scantron form? Don’t forget to use the correct units in the work-out problems!