Question

An elevator that starts from rest and moves upward as a result of a force. It moves a total distance of 10m in 3 seconds. If the mass of the elevator is 30kg, what is the tension T in the string while the elevator is moving? Assume that g=9.8 m/sec^2.

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Answer 1

First, draw the 'free body diagram' of the elevator!

Net force on elevator = (mass of elevator) × acceleration

$\implies \rm F_{net} = ma$

$\implies \rm F_{driving}- F_{opposing} = ma$

$\implies \rm T - mg = ma$

$\implies \rm T = mg + ma = m(g+a)$

•• Finding acceleration:

• s = ut + ½at²
• 10 = 0 + ½(a)3²
• 10 = ½(a) × 9
• a = 20/9 = 2.23 m/s²

$\implies \rm T = m(g+a) = 30(9.8 + 2.23)$

$\implies \rm T = 30(12.03)$

$\implies \bf T \approx 360\: N$

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