A person with a mass of 78 kg is riding in an elevator which is accelerating upward at 1.80 m/s^2.What is the person's apparent weight? A) 900 N B) 760 N C) 620 N D) 960 N
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Apparent weight means the weight of an object when moving vertically.
So, to solve for weight of the person while the elevator is moving upward, apply the formula of Newton's Second Law which is:
`sumF=ma`
Note that the forces acting on the person are its weight (W) and the tension (T) of the cable attached to the elevator. The direction of these two forces are opposite of each other. The upward force is the tension while the weight is the downward force. So,
`T - W = ma`
Since the elevator is moving up which is against the direction of gravity, then, the sign of the given acceleration is negative.
`T - W = 78(-1.8)`
`T - W = -140.4`
Moreover, the tension of the cable attached to the elevator is equal to the weight it is carrying. Note that this is the weight of the person when at rest or not moving.
`78*9.8 - W = -140.4`
`764.4 - W = -140.4`
From here, isolate W.
`W = 764.4+140.4`
`W=904.8`
Hence the apparent weight of the person when moving up is 904.8 N.
Among choices, the nearest answer is (A)900N.