It takes the elevator in a skyscraper 4.0 s to reach its cruising speed of 10m/s. A 60 kg passenger gets aboard on the ground floor. What is the passenger's apparent weight
a. Before the elevator starts moving?
b. While the elevator is speeding up?
c. After the elevator reaches its cruising speed?
a.
To find: The apparent weight of the passenger before the elevator starts moving.
Answer to Problem 19P
Solution: The apparent weight of the passenger before the elevator starts moving is
Explanation of Solution
Given data:
Mass of the passenger
Cruising speed of the elevator is
Time taken by the elevator to reach its cruising speed is 4.0 s.
Formula used:
The expression for apparent weight of the passenger before the elevator starts moving is as follows:
Here,
Two forces act on the passenger along a single vertical line. They are the downward pull of the gravity and the upward push of the elevator.
The elevator is at rest and so is the passenger before the elevator starts moving up. Therefore, the acceleration of the passenger before the elevator starts moving is
Calculation of apparent weight of the passenger before the elevator starts moving:
Substitute 60 kg for
Conclusion:
Thus, the apparent weight of the passenger before the elevator starts moving is
b.
To find: The apparent weight of the passenger while the elevator is speeding up.
Answer to Problem 19P
Solution: The apparent weight of the passenger while the elevator is speeding up is
Explanation of Solution
The expression to find the acceleration is as follows:
Here,
The speed of the elevator initially is
Therefore, the initial speed of the elevator is
And, the final speed of the elevator is
Calculation of acceleration:
Substitute
Calculation of apparent weight of the passenger, while the elevator is speeding up:
Substitute 60 kg for
Conclusion:
Thus, the apparent weight of the passenger while the elevator is speeding up is
c.
To find: The apparent weight of the passenger after the elevator reaches its cruising speed.
Answer to Problem 19P
Solution:
The apparent weight of the passenger after the elevator reaches its cruising speed is
Explanation of Solution
As the elevator does not accelerate anymore after it reaches its cruising speed, the acceleration of the passenger is
Calculation of apparent weight of the passenger after the elevator reaches its cruising speed:
Substitute 60 kg for
Conclusion:
Thus, the apparent weight of the passenger after the elevator reaches its cruising speed is
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