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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 tension in the rope?
20,600 j
23,100 j
8,230 j
15,400 j

Explanation:

Step1: Find the tension force

According to Newton's second law \(F = ma\), where \(F=T - mg\) ( \(T\) is tension, \(m = 150\space kg\), \(g=9.8\space m/s^{2}\), \(a = 1.20\space m/s^{2}\)).

$$T=m(a + g)$$

$$T=150\times(1.20+9.8)$$

$$T=150\times11$$

$$T = 1650\space N$$

Step2: Calculate the work done

The formula for work is \(W = Fd\cos\theta\). Here, \(\theta = 0^{\circ}\) (force and displacement are in the same direction), \(d = 14.0\space m\), \(F=T\).

$$W=T\times d$$

$$W=1650\times14$$

$$W = 23100\space J$$

Answer:

23,100 J