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Mech Motion in two dimensionsHW . .. .20
t J . /
2. Each diagram below shows the velocity and acceleration for an
object at a certain instant in time.Instant 1 Instant 2 Instant
4nstant 3
Acceleration t t f _ _ _ _ _ . . .Velocity
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Motion in two dimensions
3. An object moves clockwise along the trajectory below (top
view shown). The acceleration varies;but is always directed toward
point K.a. On the diagram below, indicate the direction of the
acceleration at each of the points A-G.
Top view
b. For each of the points A-G, state whether the object is
speeding up, slowing down, or neither.c. On the diagram below, draw
a velocity vector for each of the points A-G. The
relativemagnitudes of these vectors should be qualitatively
correct.
Top view
G
4. Suppose that an object were to move at constant speed around
anS-shaped curve as shown at right. The S-shaped curve is made of
twohalf circles and a straight segment.At each of the indicated
points on the diagram, draw a vector torepresent the acceleration
of the object. Ifthe magnitude of theacceleration is zero at any of
these points, indicate so explicitly.
Top view
Acceleration vectors forconstant speed
Tutorials in Introductory PhysicsMcDermott, Shaffer, and the
P.E.G., U. Wash.
Y."" : 'PearSd r lCustom 2ndEd.i forTJ:COi,Soulder.
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Motion in two dimensions Name ~ ~~
6. A car travels clockwise once around the track shown below.
Starting from rest at point A, thecatispeeds up at a constant rate
until it is just past point C. By the time it reaches point D, it
istraveling at a constant speed. Itthen travels at a constant speed
the rest of the way around thetrack.a. On the diagram at right,
indicate the direction ofthe acceleration at each ofthe points
A-G. If it ispossible to indicate theexact direction of
theacceleration, do so, andwrite "E" for exact.Otherwise, indicate
theapproximate direction ofthe acceleration. Ifthemagnitude of
theacceleration is zero at anypoint(s), state soexplicitly.
, . . . . . "
b. Is the magnitude of the acceleration at point G greater than,
less than, or equal to that atpoint D? Explain.
7. Write a vector equation (e.g., i 5 + E + F = 0 ) that relates
the vectors Ii,B , and Cshown at right. . ~. ~A . - r c ~ - bOn the
grid at right, draw a diagram that shows how to find the vector7
that must be added to g to give the vector h. Clearly label
thisvector.
Tutorials in Introductory Physics. McDermott; Shaffer, and the
PEG., U. Wash.
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Mech Motion in two dimensionsHW-24
CaseC. Three cars move at constantspeed around three
circulartracks as shown in the top-view diagram at right.In cases A
and B,the radiusof the track is R; in case C,2R. In case A, the
speed ofthe car is 2vo: in cases Band C, vo '
Case A CaseB
o o vo20o
a. Rank the three cases according to magnitude oj acceleration,
from largest to smallest. If themagnitude of the acceleration is
the same in any of the cases, state so explicitly, Explain
yourreasoning using the general rules you devised in tutorial.\ f
< -I ~ \ : : .~
b. Explain how your ranking above is consistent with the result
for the magnitude of theacceleration for the case of uniform
circular motion: a = v2/r, where v is the speed of theobject and r
is the radius of the circular trajectory,\
Tutorials in Introductory PhysicsMcDennott, Shaffer, and the
P.E.G" U. Wash. PearsonCustom 2 . " d Ed., for nco, Boulder
f '
