Question

if sneezy hangs from a similar rope while delivering presents at the earth's equator, what will the tension in it be? (recall that the earth is rotating about an axis through its north and south poles.) express your answer to four significant figures and include the appropriate units.

Answer 1

The tension in the rope at the Earth's equator will be the difference between the gravitational force acting on the object and the centripetal force due to Earth's rotation. To calculate it, we require the object's mass. The tension is given in Newtons.

Step-by-step explanation:

To determine the tension in a rope at the Earth's equator due to the Earth's rotation, we need to take into account the centripetal force required to keep the object moving in a circle with the Earth’s rotation. The centripetal force, which is directed towards the center of the rotation (in this case, the axis through the North and South poles), reduces the effective gravitational force on the object. The actual tension in the rope would be the difference between the gravitational force and the centripetal force required for circular motion at the Earth's equator.

Let's denote:

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The gravitational force (Fg) acting on the object is:

Fg = M × g

To calculate the centripetal force (Fc), we use:

Fc = M × ω² × R

The tension in the rope (T) is then:

T = Fg - Fc

To calculate the exact tension, we would need the mass of sneezy or the presents. Assuming that mass (M) is known, the tension can be calculated with the above steps. The resultant tension will have units in Newtons (N).