Question

question 13
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 tension in the rope?
150 n
1,470 n
1,650 n
180 n

Explanation:

Step1: Apply Newton's second law

Newton's second law is \(F = ma\). The forces acting on the basket are the tension \(T\) (upward) and the weight \(mg\) (downward). So, \(T - mg=ma\).

Step2: Solve for tension \(T\)

Rearrange the equation \(T - mg = ma\) to get \(T=m(a + g)\). Given \(m = 150\space kg\), \(a=1.20\space m/s^{2}\), and \(g = 9.8\space m/s^{2}\). Substitute the values: \(T=150\times(1.20 + 9.8)\).

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Answer:

1,650 N