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As part of an outdoor display, a 5-kg model of the Earth is attached to wires AC and BC and revolves at a constant speed [tex]v[/tex] in the horizontal circle shown. Determine the range of the allowable values of [tex]v[/tex] if both wires are to remain taut and if the tension in either of the wires is not to exceed 116 N.

Given: [tex]r[/tex]

Answer :

These disparities presuppose that the system is friction-free and that the wires are precisely vertical. The actual range of permitted values for v may differ slightly from these specifications in practice.

[tex]T1 = mg + mv^2/rT2 = mg - mv^2/r[/tex]

The tension in wire BC is at its highest point when the model is at the bottom of the circle, while the tension in wire AC is at its lowest point.

[tex]T1 = mg - mv^2/rT2 = mg + mv^2/rT1 ≥ 0T2 ≥ 0T1 ≤ 116 NT2 ≤ 116 N[/tex]

Substituting the expressions for T1 and T2, we get:

[tex]mg - mv^2/r ≥ 0mg + mv^2/r ≥ 0mg + mv^2/r ≤ 116 Nmg - mv^2/r ≤ 116 N[/tex]

Simplifying these inequalities, we get:

[tex]v^2 ≤ mgr/5v^2 ≥ mgr/7v^2 ≤ 116r/m + mgr/5v^2 ≥ mgr/7 - 116r/m[/tex]

Therefore, the allowable range of values for v is:

[tex]sqrt(mgr/7) ≤ v ≤ sqrt(mgr/5)[/tex]

or approximately:

14.2 m/s ≤ v ≤ 17.7 m/s

How fast is the Earth moving per km/hour?

To solve this, follow these steps! Due to the fact that the Earth rotates once every 23h 56m (23.933h), at the equator where its circle is 2R = 2x3, 14x6378 km = 40,000 km, it must move at a speed of Vrot = 40000km/23.933h = 1,674 km/hr.

to know more about speed range here:

brainly.com/question/30372715

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