If the error in the angle is 0.50, the error in sin 90° is
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We have to forces acting on the system (elevator+passengers):
1) The weight (W=5000 N), acting downward
2) The cable's tension (T=6000 N), acting upward
So, the two forces have opposite direction. The resultant (in upward direction) will be
And for Newton's second law, the resultant of the forces acting on the system causes an acceleration on the system itself, given by
where m is the mass of the system.
So, we need to find F and m.
The resultant of the forces is
To find m, we can use the weight of the system. In fact, the weight of an object is given by
where
. Solving for m, and using W=5000 N, we find
and at this point, we can calculate the acceleration of the system (elevator+people):
and the acceleration has the same direction of the resultant force, so upward.
1) The weight (W=5000 N), acting downward
2) The cable's tension (T=6000 N), acting upward
So, the two forces have opposite direction. The resultant (in upward direction) will be
And for Newton's second law, the resultant of the forces acting on the system causes an acceleration on the system itself, given by
where m is the mass of the system.
So, we need to find F and m.
The resultant of the forces is
To find m, we can use the weight of the system. In fact, the weight of an object is given by
where
and at this point, we can calculate the acceleration of the system (elevator+people):
and the acceleration has the same direction of the resultant force, so upward.