A 60-kg person stands on a scale in an elevator. How many newtons does the scale read (a) when the elevator is ascending with an acceleration of 1 m/s 2 ; (b) when it is descending with an acceleration of 1 m/s 2 ; (c) when it is ascending at a constant speed of 3 m/s; (d) when it is descending at a constant speed of 3 m/s; (e) when the cable has broken and the elevator is descending in free fall?
A 60-kg person stands on a scale in an elevator. How many newtons does the scale read (a) when the elevator is ascending with an acceleration of 1 m/s 2 ; (b) when it is descending with an acceleration of 1 m/s 2 ; (c) when it is ascending at a constant speed of 3 m/s; (d) when it is descending at a constant speed of 3 m/s; (e) when the cable has broken and the elevator is descending in free fall?
A 60-kg person stands on a scale in an elevator. How many newtons does the scale read (a) when the elevator is ascending with an acceleration of 1 m/s2; (b) when it is descending with an acceleration of 1 m/s2; (c) when it is ascending at a constant speed of 3 m/s; (d) when it is descending at a constant speed of 3 m/s; (e) when the cable has broken and the elevator is descending in free fall?
(a)
Expert Solution
To determine
The reading on the scale when the elevator is ascending with an acceleration of 1m/s2.
Answer to Problem 60E
The reading on the scale when the elevator is ascending with an acceleration of 1m/s2 is 648N.
Explanation of Solution
Given Info: The mass of the person is 60kg.
Write the expression for the force.
F=mg+ma
Here,
F is the force.
m is the mass.
a is the acceleration.
g is the acceleration due to gravity.
Substitute 60kg for m, 1m/s2 for a and 9.8m/s2 for g to find F.
F=(60kg)(9.8m/s2)+(600kg)(1m/s2)=648N
Conclusion:
Therefore, the reading on the scale when the elevator is ascending with an acceleration of 1m/s2 is 648N.
(b)
Expert Solution
To determine
The reading on the scale when the elevator is descending with an acceleration of 1m/s2.
Answer to Problem 60E
The reading on the scale when the elevator is descending with an acceleration of 1m/s2 is 528N.
Explanation of Solution
Given Info: The mass of the person is 60kg.
Write the expression for the force.
F=mg−ma
Substitute 60kg for m, 1m/s2 for a and 9.8m/s2 for g to find F.
F=(60kg)(9.8m/s2)−(600kg)(1m/s2)=528N
Conclusion:
Therefore, the reading on the scale when the elevator is descending with an acceleration of 1m/s2 is 528N.
(c)
Expert Solution
To determine
The reading on the scale when the elevator is ascending at a constant speed of 3m/s2.
Answer to Problem 60E
The reading on the scale when the elevator is ascending at a constant speed of 3m/s2 is 588N.
Explanation of Solution
Given Info: The mass of the person is 60kg.
Write the expression for the force.
F=mg
Substitute 60kg for m and 9.8m/s2 for g to find F.
F=(60kg)(9.8m/s2)=588N
Conclusion:
Therefore, the reading on the scale when the elevator is ascending at a constant speed of 3m/s2 is 588N.
(d)
Expert Solution
To determine
The reading on the scale when the elevator is descending at a constant speed of 3m/s2.
Answer to Problem 60E
The reading on the scale when the elevator is descending at a constant speed of 3m/s2 is 588N.
Explanation of Solution
Given Info: The mass of the person is 60kg.
Write the expression for the force.
F=mg
Substitute 60kg for m and 9.8m/s2 for g to find F.
F=(60kg)(9.8m/s2)=588N
Conclusion:
Therefore, the reading on the scale when the elevator is descending at a constant speed of 3m/s2 is 588N.
(e)
Expert Solution
To determine
The reading on the scale when the cable has broken, and the elevator is descending in freefall.
Answer to Problem 60E
The reading on the scale when the cable has broken, and the elevator is descending in freefall is zero.
Explanation of Solution
Given Info: The mass of the person is 60kg.
When the object is in freefall, the object feels weightless. This is because the acceleration of the object is same as the acceleration due to gravity. And thus, the object is weightless.
For the person in the lift, the reading on the scale depends on the acceleration of the lift. In freefall, the person feels no weight. And the reading on the scale is zero.
Conclusion:
Therefore, the reading on the scale when the cable has broken, and the elevator is descending in freefall is zero.
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