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Chapter 4 Question 4
a. The weight of an object on the Earth is the gravitational pull of the Earth on the
object. Explain why a spring balance does not faithfully indicate the weight of the
objects near the equator, no matter how precise the spring balance is. Discuss how
the weight of an object varies as the object is moved from the equator to one of the
poles.
All objects on the Earth are performing circular motion, i.e. the net forces of all
objects are non-zero. The net force (also called centripetal force) is the difference
between gravitational pull and the force of support.
In the case of a spring balance hanging a mass, the force of support (namely, the
tension) is provided by the spring balance.
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marks
1
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In the above diagram, the object is hung at the equator:
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Thus, the spring balance cannot give exactly the gravitational pull.
From equation (1), the centripetal force is smaller for smaller radius of path. As an
object is moved from the equator, the radius of path decreases.
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Thus, the centripetal force is smaller as the object is moved to the pole, i.e. the
difference between tension and the gravitational pull is decreased.
Hence, the reading in the spring balance increases as the object is moved to the
pole.
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b. With the aid of a diagram, illustrate how the string that suspends a mass freely at
latitude q deviates from the line joining the mass and the Earth’s center. On your
diagram, clearly indicate the resultant force acting on the mass.
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marks
The gravitational pull FG is always pointing towards the Earth's center.
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The direction of the tension FB in the string acts such that the vector sum of FB and
the gravitational pull FG is pointing to and at right angle to the Earth's axis.
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c. State the definition for the Earth’s gravitational field strength g. Explain how the value
of g varies with the distance from the Earth’s center, stating any necessary
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assumptions.
marks
The Earth's gravitational field strength is the gravitational force acting on any
object per unit mass of the object:
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Outside the Earth (Fig.4.4.3)
The Earth can be regarded as a point mass at the centre. Thus the field strength is
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Below the Earth (Fig.4.4.4)
The effective mass of the Earth that attract any mass is the smaller sphere:
Thus, the field strength inside is
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Graphical representation
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d. For a satellite revolving round the Earth in a circular orbit of radius r and with period 3
T, show that r3 = kT2 where k is a constant.
marks
At the orbit of radius r, the gravitational force acting on the satellite of mass m is
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For circular orbit, this force is exactly the centripetal force
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