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6.3 Gravitational potential energy and gravitational potential (SB p. 215)
The gravitational potential energy (U) of a body of mass m at a point in a gravitational field is defined as the negative of work done by the gravitational force to bring the body from infinity to that point.
6.3 Gravitational potential energy and gravitational potential (SB p. 217)
The gravitational potential (V) at a point in a gravitational field is the work done by the gravitational force to bring a unit mass from infinity to that point.
6.3 Gravitational potential energy and gravitational potential (SB p. 220)
Relationship between V, g and r
Note: The gravitational field strength (g) is actually a vector and its value should be negative to represent its direction. In section 6.2, g is positive since we consider its magnitude only.
The gravitational potential energy (U) of two particles at infinite separation is defined as zero by convention. Hence, U must be negative or zero (at infinity).
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6.3 Gravitational potential energy and gravitational potential (SB p. 216)
Q:Q: The dashed lines in the figure represent the equipotential lines around the earth. The gravitational potential is as shown for each of the equipotential lines.
6.3 Gravitational potential energy and gravitational potential (SB p. 219)
Q:Q: (a) (i) Which one of the points (or points) has the highest gravitational potential? Explain your answer.
(ii) Calculate the work done by the gravitational field in bringing a spacecraft of mass 5 000 kg (1) from A to C; (2) from C to D.(b) (i) The equipotential lines, which are given
every 0.5 × 107 J kg−1, are not equally spaced. Explain why.
(ii) Calculate the distances AB and BC.( G = 6.7 × 10−11 N kg−2 m2; mass of earth = 6.0 × 1024 kg)
Solution
6.3 Gravitational potential energy and gravitational potential (SB p. 219)
Q:Q: (a) Explain what is meant by(i) gravitational field strength, and(ii) gravitational potential.
Give an expression for each of these physical quantities and an equation relating the two quantities.(b) Show that the values of the gravitational field strength and the gravitational potential at any point of the earth’s surface are g and gRE respectively.Assume that the earth is a uniform surface of radius RE; and g is the acceleration of free fall on the earth’s surface.
6.3 Gravitational potential energy and gravitational potential (SB p. 221)
(a) (i) The gravitational field strength at a point in a gravitational field is the gravitational force acted on a unit mass at that point.
(ii) The gravitational potential (V) at a point in a gravitational field is the work done by the gravitational force to bring a unit mass from infinity to that point.
6.3 Gravitational potential energy and gravitational potential (SB p. 221)