An elevator can move upwards at a maximum acceleration of 2 m/s/s. If the cable

Question

An elevator can move upwards at a maximum acceleration of 2 m/s/s. If
the cable pulling up the elevator car can stand a maximum tension in it
of 1,000 N, how many people (each of mass 50 kg) can safely ride in the
elevator when it is moving up at that maximum acceleration? Ignore the
mass of the elevator. Hint: Assume that the maximum number of people in
the elevator is X. Then, find the force due to gravity acting on these
people before finding the resultant force on them when the elevator
begins to ascend. After this apply Newton’s 2nd Law to solve for the
answer.

Explanation / Answer

Maximum acceleration a = 2 m / s^ 2 Maximum tension T = 1000 N Mass of each m = 50 kg In upward motion , T = M( a+ g ) = M ( 2 + 9.8 ) = 11.8 M Total mass supported M = T / 11.8 = 84.74 kg So, require number of persons N = M / m = 1.69 So, maximum persons = 1

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