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problem reference 6.2
a hot air balloon lifts a 150 kg basket straight up by means of a rope. the basket has an upward acceleration of 1.20 m/s² and is lifted from rest a distance of 14.0 m.
what is the work done by the persons weight?
-14,700 j
-33,100 j
-20,600 j
-23,100 j

Explanation:

Step1: Calculate the weight of the basket

The weight \(F = mg\), where \(m = 150\space kg\) and \(g=9.8\space m/s^{2}\).
\(F=150\times9.8 = 1470\space N\)

Step2: Determine the angle between force and displacement

The weight acts downward and the displacement is upward, so \(\theta = 180^{\circ}\), and \(\cos\theta=- 1\)

Step3: Calculate the work done

The work - done formula is \(W = Fd\cos\theta\). Given \(d = 14.0\space m\)
\(W=1470\times14\times(-1)=-20580\space J\approx - 20600\space J\)

Answer:

-20,600 J