Physics 2A -Sec X - Final Exam (winter 2012)
Instructor: Benjamin Grinstein

Name: ___________________________________    3-digit personal No: _____________    Date: ______________
Write your name, and code number above and on your scantron over the line labeled "NAME".
Bubble in your code number in the scantron in the space labeled "EXAM NUMBER" (always use a No 2 pencil. on the scnatron).
Bubble in the version of your test (a letter, A-D), found at the botton of this page, on your scantron in the space labeled "TEST FORM."

Unless otherwise instructed, use g = 9.8 m/s2

Rotational Inertia about an axis through com:
Hoop about axis(radius=R, mass=M) : MR2
Hoop about diameter (radius=R, mass=M): 1/2MR2
Disk/solid cyllinder about central axis(radius=R, mass=M, length=L): 1/2MR2
Disk/solid cyllinder about axis perpendicular to length, that is, central diameter (radius=R, mass=M, length=L): 1/4MR2+1/12ML2
Thin rod about axis perpendicular to length (mass=M, length = L): 1/12ML2
Solid sphere about diameter (radius=R, mass=M): 2/5MR2
Thin spherical shell about diameter (radius=R, mass=M): 2/3MR2
Rectangular slab about perpendicular axis (mass=M, sides: a, b): 1/12M(a2+b2)

Solve the following problems. Enter the answers in your scantron (always use a No 2 pencil. on the scnatron).



1.
Two bodies are falling with negligible air resistance, side by side, above a horizontal plane. If one of the bodies is given an additional horizontal acceleration during its descent, it:
A.
strikes the plane at the same time as the other body
B.
strike the plane earlier than the other body
C.
has the vertical component of its velocity altered
D.
has the vertical component of its acceleration altered
E.
follows a straight line path along the resultant acceleration vector


2.
A boat is traveling upstream at 14 mph with respect to a river that is flowing at 6 mph (with respect to the ground). A man runs directly across the boat, from one side to the other (left/right sides, not front/back!!), at 6 mph (with respect to the boat). The speed of the man with respect to the ground is:
A.
10 mph
B.
14 mph
C.
18.5 mph
D.
21 mph
E.
26 mph


3.
Two blocks with masses m and M are pushed along a horizontal frictionless surface by a horizontal applied force as shown. The magnitude of the force of either of these blocks on the other is:
A.
mF/(m + M)
B.
mF/M
C.
mF/(M – m)
D.
MF/(M + m)
E.
MF/m


4.
A coin is placed on a horizontal phonograph turntable. Let N be the normal force exerted by the turntable on the coin, f be the frictional force exerted by the turntable on the coin, and fs, max be the maximum force of the static friction. The speed of the turntable is increased in small steps. If the coin does not slide, then
A.
N increases, f increases, and fs, max stays the same
B.
N increases, f increases, and fs, max increases
C.
f increases and both N and fs, max stay the same
D.
N, f, and fs, max all stay the same
E.
N, f, and fs, max all increase


5.
A stone is thrown horizontally and follows the path XYZ shown. The direction of the acceleration of the stone at point Y is:
A.
↓
B.
→
C.
D.
E.


6.
A block is attached to the end of an ideal spring and moved from coordinate xi to coordinate xf. The relaxed position is at x = 0. The work done by spring is positive if:
A.
xi = 2 cm and xf = 4 cm
B.
xi = –2 cm and xf = 4 cm
C.
xi = –2 cm and xf = –4 cm
D.
xi = 2 cm and xf = –4 cm
E.
xi = –4 cm and xf = –2 cm


7.
A crate moves 10 m to the right on a horizontal surface as a woman pulls on it with a 10-N force. Rank the situations shown below according to the work done by her force, least to greatest.
A.
1,2,3
B.
2,1,3
C.
2,3,1
D.
1,3,2
E.
3,2,1,


8.
At time t = 0 a particle starts moving along the x axis. If its kinetic energy increases uniformly with t the net force acting on it must be:
A.
constant
B.
proportional to t
C.
inversely proportional to t
D.
E.


9.
Two particles interact by conservative forces. In addition, an external force acts on each particle. They complete round trips, ending at the points where they started. Which of the following must have the same values at the beginning and end of this trip?
A.
the total kinetic energy of the two-particle system
B.
the potential energy of the two-particle system
C.
the mechanical energy of the two-particle system
D.
the total linear momentum of the two-particle system
E.
none of the above


10.
A ball of mass m, at one end of a string of length L, rotates in a vertical circle just fast enough to prevent the string from going slack at the top of the circle. Denote the downward pointing gravitational acceleration by g. The speed of the ball at the bottom of the circle is:


Answer:


11.
The potential energy of a particle moving along the x axis is given by

   U(x) = (8.0J/m2)x2 + (2.0J/m4)x4.

If the total mechanical energy is 9.0 J, the limits of motion are:
A.
–0.96 m; +0.96 m
B.
–2.2 m; +2.2 m
C.
–1.6 m; +1.6 m
D.
–0.96 m; +2.2 m
E.
–0.96 m; +1.6 m


12.
The diagram shows a plot of the potential energy as a function of x for a particle moving along the x axis. The points of neutral equilibrium are:
A.
only a
B.
only b
C.
only c
D.
only d
E.
b and d


13.
The x and y coordinates in meters of the center of mass of the three-particle system shown below are:
A.
0, 0
B.
1.3 m, 1.7 m
C.
1.4 m, 1.9 m
D.
1.9 m, 2.5 m
E.
1.4 m, 2.5 m


14.
Two 4.0-kg blocks are tied together with a compressed spring between them. They are thrown from the ground with an initial velocity of 35 m/s, 45° above the horizontal. At the highest point of the trajectory they become untied and spring apart. About how far below the highest point is the center of mass of the two-block system 2.0 s later, before either fragment has hit the ground?
A.
12 m
B.
20 m
C.
31 m
D.
Can't tell because the velocities of the fragments are not given.
E.
Can't tell because the coordinates of the highest point are not given.


15.
A very massive object traveling at 10 m/s strikes a light object, initially at rest, and the light object moves off in the direction of travel of the heavy object. If the collision is elastic, the speed of the lighter object is, to good approximation (Hint: Recall the discussion of the basketball-tennisball collision in class)
A.
5.0 m/s
B.
10 m/s
C.
15 m/s
D.
20 m/s
E.
Can't tell from the information given.


16.
A sphere and a cylinder of equal mass and radius are simultaneously released from rest on the same inclined plane sliding down the incline. Then:
A.
the sphere reaches the bottom first because it has the greater inertia
B.
the cylinder reaches the bottom first because it picks up more rotational energy
C.
the sphere reaches the bottom first because it picks up more rotational energy
D.
they reach the bottom together
E.
none of the above is true


17.
A hoop, a uniform disk, and a uniform sphere, all with the same mass and outer radius, start with the same speed and roll without sliding up identical inclines. Rank the objects according to how high they go, greatest to least.
A.
hoop, disk, sphere
B.
disk, hoop, sphere
C.
sphere, hoop, disk
D.
sphere, disk, hoop'
E.
hoop, sphere, disk


18.
A rod rests on frictionless ice. Forces that are equal in magnitude and opposite in direction are simultaneously applied to its ends as shown. The quantity that vanishes is its:
A.
angular momentum
B.
angular acceleration
C.
total linear momentum
D.
kinetic energy
E.
rotational inertia


19.
A pulley with radius R and rotational inertia I is free to rotate on a horizontal fixed axis through its center. A string passes over the pulley. A block of mass m1 is attached to one end and a block of mass m2, is attached to the other. At one time the block with mass m1 is moving downward with speed v. If the string does not slip on the pulley, the magnitude of the total angular momentum, about the pulley center, of the blocks and pulley, considered as a system, is given by:
A.
(m1 – m2)vR + Iv/R
B.
(m1 + m2)vR + Iv/R
C.
(m1 – m2)vR – Iv/R
D.
(m1 + m2)vR – Iv/R
E.
none of the above


20.
A man, holding a weight in each hand, stands at the center of a horizontal frictionless rotating turntable. The effect of the weights is to double the rotational inertia of the system. As he is rotating, the man opens his hands and drops the two weights. They fall outside the turntable. Then:
A.
his angular velocity doubles
B.
his angular velocity remains about the same
C.
his angular velocity is halved
D.
the direction of his angular momentum vector changes
E.
his rotational kinetic energy increases


21.
A meter stick on a horizontal frictionless table top is pivoted at the 80-cm mark. A force is applied perpendicularly to the end of the stick at 0 cm, as shown. A second force (not shown) is applied perpendicularly at the 100-cm end of the stick. The forces are horizontal. If the stick does not move, the force exerted by the pivot on the stick:
A.
must be zero
B.
must be in the same direction as and have magnitude
C.
must be directed opposite to and have magnitude
D.
must be in the same direction as and have magnitude
E.
must be directed opposite to and have magnitude


22.
A 5.0 m weightless strut, hinged to a wall, is used to support a 800-N block as shown. The horizontal and vertical components of the force of the hinge on the strut are:
A.
FH = 800 N, FY = 800 N
B.
FH = 600 N, FY = 800 N
C.
FH = 800 N, FY = 600 N
D.
FH = 1200 N, FY = 800 N
E.
FH = 0 , FY = 800 N


23.
A uniform sphere of radius R rotates about a diameter with angular momentum of magnitude L. Under the action of internal forces the sphere collapses to a uniform sphere of radius R/2. The magnitude of its new angular momentum is:
A.
L/4
B.
L/2
C.
L
D.
2L
E.
4L


24.
An 80-N uniform plank leans against a frictionless wall as shown. The torque (about point P) applied to the plank by the wall is:
A.
40 N⋅m
B.
60 N⋅m
C.
120 N⋅m
D.
160 N⋅m
E.
240 N⋅m


25.
A mass-spring system is oscillating with amplitude A. The kinetic energy will equal the potential energy only when the displacement is
A.
zero
B.
± A/4
C.
D.
± A/2
E.
anywhere between –A and +A


26.
A meter stick is pivoted at a point a distance a from its center and swings as a physical pendulum. Of the following values for a, which results in the shortest period of oscillation?
A.
a = 0.1 m
B.
a = 0.2 m
C.
a = 0.3 m
D.
a = 0.4 m
E.
a = 0.5 m


27.
A particle moves in simple harmonic motion according to x = 2cos(50t), where x is in meters and t is in seconds. Its maximum velocity in m/s is:
A.
100 sin(50t)
B.
100 cos(50t)
C.
100
D.
200
E.
none of these


28.
For an oscillator subjected to a damping force proportional to its velocity:
A.
the displacement is a sinusoidal function of time
B.
the velocity is a sinusoidal function of time
C.
the frequency is a decreasing function of time
D.
the mechanical energy is constant
E.
none of the above is true


29.
A block attached to a spring undergoes simple harmonic motion on a horizontal frictionless surface. Its total energy is 50 J. When the displacement is half the amplitude, the kinetic energy is:
A.
zero
B.
12.5 J
C.
25 J
D.
37.5 J
E.
50 J


30.
An object on the end of a spring is set into oscillation by giving it an initial velocity while it is at its equilibrium position. In the first trial the initial velocity is v0 and in the second it is 4v0. In the second trial:
A.
the amplitude is half as great and the maximum acceleration is twice as great
B.
the amplitude is twice as great and the maximum acceleration is half as great
C.
both the amplitude and the maximum acceleration are twice as great
D.
both the amplitude and the maximum acceleration are four times as great
E.
the amplitude is four times as great and the maximum acceleration is twice as great


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