1.
[6] Shown on the right is the x - t graph of a
particle undergoing rectilinear motion along the
x axis.
In each of the questions below, circle the
point(s) for which each statement is true. Note
that points P and R are points of inflection.
a) The velocity is greater than zero.
P
Q
R
S
b) The velocity is less than zero.
P
Q
R
S
c) The velocity is equal to zero.
P
Q
R
S
d) The speed is the greatest.
P
Q
R
S
e) The acceleration is positive.
P
Q
R
S
f) The acceleration is negative.
P
Q
R
S
2.
An object falls freely from height h and strikes the ground T seconds later.
a) [1] When the object is at 0.5h above ground level, is the elapsed time less than
0.5T, equal to 0.5T, or greater than 0.5T? (Circle one)
Less
Equal
Greater
b) [1] When the elapsed time is 0.5 T, is the height of the object less than 0.5 h,
equal to 0.5 h, or greater than 0.5 h above ground level? (Circle one)
Less
Equal
Greater
c) [1] Suppose now that you drop the object from rest at height h and it strikes the
ground with speed v0. At the same time you drop it, your friend throws an
identical object with an initial speed v0 upwards from ground level. At some
height, the objects pass each other. Is this point less than 0.5 h, equal to 0.5 h,
or greater than 0.5 h above ground level? (Circle one)
Less
Equal
Greater
3.
Consider the system shown consisting of blocks A, B
and C. The friction between A and the horizontal
surface is sufficient to prevent A from sliding, while the
friction between A and B is not sufficient to prevent B
from sliding on A.
In each of the questions below, indicate clearly the
correct directions of any vector (horizontal, vertical,
perpendicular or parallel to the incline, etc.) on each
diagram. All symbols shown on your diagrams are to be assumed to take on positive
values. Use the symbols FS and FK to indicate static and kinetic friction forces
respectively. T
a) [3] Draw the free-body and kinetic diagrams (FBD/KD) for block A.
b) [3] Draw the free-body and kinetic diagrams (FBD/KD) for block B.
4.
A particle moves along an axis (horizontal axis) so that its velocity varies as
v = 15 e
-kx
where k is a constant, x is in meters, and v is in m/s. At t = 1 sec, the particle passes
the origin.
a) [2] If v = 10 m/s when x = 2 m, determine k (be sure to indicate the proper units).
(b) [3] Determine the acceleration of the particle when x = 3 m.
(c) [4] Determine the position of the particle when x = 4 m.
Note:
5.
You are playing catch with a friend in the hallway of your dormitory. The distance
from floor to ceiling is D and you throw the ball with an initial speed of at
some angle with respect to the horizontal floor.
[8] What is the maximum horizontal distance (in terms of D) that the ball can travel
before it bounces for the first time? You may assume that the ball is launched from
the floor.
6.
A particle moves along the path given by y = cos() where both x and y are
measured in meters. At the point on the curve where x = 0.5 m the speed is
2
observed to be 3 m/s and the speed is increasing at a rate of 2 m/s .
a) [5] Determine the magnitude of the acceleration at the point where x = 0.5 m.
b) [4] At this same point (x = 0.5 m), determine the angle between the velocity and
acceleration vectors.
7.
For the system shown, the relative velocity of block B with
respect to point A, which is fixed to the rope, is vB/A = 3 m/s,
where this relative velocity is directed at an angle of 70
above the nearest horizontal.
[3] Determine the constraint equations relating the speeds
of blocks A and B.
[6] Determine the velocities of blocks A and B expressed in
terms of their magnitudes and clearly-indicated directions.