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42. A pendulum with a cord oflength r 1.00 m swings ina vertical plane (Fig. P4.42)When the pendulum is in thetwo horizontal positions 090.0° and 0 270°, its speed is5.00 m/s. Find the magnitudeof (a) the radial accelerationand (b) the tangential acceleration for these positions(c) Draw vector diagrams to=determine the direction of thetotal acceleration for these twoposiions. (d) Calculate themagnitude and direction ofthe total acceleration at theseFigure P4.42two positions

Question
42. A pendulum with a cord of
length r 1.00 m swings in
a vertical plane (Fig. P4.42)
When the pendulum is in the
two horizontal positions 0
90.0° and 0 270°, its speed is
5.00 m/s. Find the magnitude
of (a) the radial acceleration
and (b) the tangential accel
eration for these positions
(c) Draw vector diagrams to
=
determine the direction of the
total acceleration for these two
posiions. (d) Calculate the
magnitude and direction of
the total acceleration at these
Figure P4.42
two positions
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42. A pendulum with a cord of length r 1.00 m swings in a vertical plane (Fig. P4.42) When the pendulum is in the two horizontal positions 0 90.0° and 0 270°, its speed is 5.00 m/s. Find the magnitude of (a) the radial acceleration and (b) the tangential accel eration for these positions (c) Draw vector diagrams to = determine the direction of the total acceleration for these two posiions. (d) Calculate the magnitude and direction of the total acceleration at these Figure P4.42 two positions

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check_circleAnswer
Step 1

Part A:

The cord length of the pendulum is 1.00 m
swings in a vertical plane and speed is
5.00 m/s.
Write the formula to calculate the radial
acceleration
Here, v is the speed of cord, r is the length
of the cord and a is the radial acceleration
of the cord
help_outline

Image Transcriptionclose

The cord length of the pendulum is 1.00 m swings in a vertical plane and speed is 5.00 m/s. Write the formula to calculate the radial acceleration Here, v is the speed of cord, r is the length of the cord and a is the radial acceleration of the cord

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Step 2
Substitute 5.00 m/s for v and 1m for r to
find a.
(5.00 m/s)2
a
1m
The radial acceleration is same for both
condition at 0=90° and 0 = 270*
Conclusion
Therefore, the radial accelerations at the
both are 25.0 m/s2.
position 90
and 270
help_outline

Image Transcriptionclose

Substitute 5.00 m/s for v and 1m for r to find a. (5.00 m/s)2 a 1m The radial acceleration is same for both condition at 0=90° and 0 = 270* Conclusion Therefore, the radial accelerations at the both are 25.0 m/s2. position 90 and 270

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Step 3

Part B:...

For the pendulum, the tangential
acceleration is only due to that of gravity
and it is downward at both position
Conclusion:
Therefore, the tangential acceleration at
and 270
both the position 90
9.81 m/s2
is
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For the pendulum, the tangential acceleration is only due to that of gravity and it is downward at both position Conclusion: Therefore, the tangential acceleration at and 270 both the position 90 9.81 m/s2 is

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