A ball swings counterclockwise in a vertical circle at the end of a rope 1.50 m long. When the ball is 36.9° past the lowest point on its way up, its total acceleration is ( − 2.25 i ^ + 20.2 j ^ ) m / s 2 . For that instant, (a) sketch a vector diagram showing the components of its acceleration, (b) determine the magnitude of its radial acceleration, and (c) determine the speed and velocity of the ball.
A ball swings counterclockwise in a vertical circle at the end of a rope 1.50 m long. When the ball is 36.9° past the lowest point on its way up, its total acceleration is ( − 2.25 i ^ + 20.2 j ^ ) m / s 2 . For that instant, (a) sketch a vector diagram showing the components of its acceleration, (b) determine the magnitude of its radial acceleration, and (c) determine the speed and velocity of the ball.
Solution Summary: The author illustrates the vector diagram showing the components of acceleration in figure I.
A ball swings counterclockwise in a vertical circle at the end of a rope 1.50 m long. When the ball is 36.9° past the lowest point on its way up, its total acceleration is
(
−
2.25
i
^
+
20.2
j
^
)
m
/
s
2
. For that instant, (a) sketch a vector diagram showing the components of its acceleration, (b) determine the magnitude of its radial acceleration, and (c) determine the speed and velocity of the ball.
The de-excitation of a state occurs by competing emission and relaxation processes. If the relaxation mechanisms are very effective:a) the emission of radiation is largeb) the emission of radiation is smallc) the emission occurs at a shorter wavelengthd) the de-excitation occurs only by emission processes
m
C
A block of mass m slides down a ramp of height hand
collides with an identical block that is initially at rest.
The two blocks stick together and travel around a loop of
radius R without losing contact with the track. Point A is
at the top of the loop, point B is at the end of a horizon-
tal diameter, and point C is at the bottom of the loop, as
shown in the figure above. Assume that friction between
the track and blocks is negligible.
(a) The dots below represent the two connected
blocks at points A, B, and C. Draw free-body dia-
grams showing and labeling the forces (not com
ponents) exerted on the blocks at each position.
Draw the relative lengths of all vectors to reflect
the relative magnitude of the forces.
Point A
Point B
Point C
(b) For each of the following, derive an expression in
terms of m, h, R, and fundamental constants.
i. The speed of moving block at the bottom of
the ramp, just before it contacts the stationary
block
ii. The speed of the two blocks immediately…
The velocity of an elevator is given by the graph shown.
Assume the positive direction is upward.
Velocity (m/s)
3.0
2.5
2.0
1.5
1.0
0.5
0
0
5.0
10
15
20
25
Time (s)
(a) Briefly describe the motion of the elevator.
Justify your description with reference to the
graph.
(b) Assume the elevator starts from an initial position
of y = 0 at t=0. Deriving any numerical values
you
need from the graph:
i. Write an equation for the position as a
function of time for the elevator from
t=0 to t = 3.0 seconds.
ii. Write an equation for the position as a
function of time for the elevator from t = 3.0
seconds to t = 19 seconds.
(c) A student of weight mg gets on the elevator
and rides the elevator during the time interval
shown in the graph. Consider the force of con-
tact, F, between the floor and the student. How
Justify your answer with reference to the graph
does F compare to mg at the following times?
and your equations above.
i. = 1.0 s
ii. = 10.0 s
Chapter 4 Solutions
Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
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