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3.1 Gravitational Force Practice Problems HW KEY
Force of Gravity and Gravitational Field Strength Problems:
1. Look at the picture below, why does the girl’s weight change and the mass does not? Explain it in the
terms of MASS, WEIGHT, and GRAVITTIONAL FORCE.
Weight of an object is the amount
gravitational force (Fg) exerted on that
object. Fg = mg
It depends on the person’s mass - m (which
never changes) and the gravitational field
strength – g. g will change depending on
where you are in the universe (each planet has
a different g for example)
So, the weight of the girl is more on Earth
than on Moon because g on the Earth is
greater than on the Moon, making W or Fg
greater on Earth.
2. What is the force of gravity at the Earth 's surface on each of the following masses?
a. 75.0 kg
735 N
d. 3.14 kg
30.8 N
b. 454 g
4.45 N
e. 0.382 kg
3.74 N
c. 2.00 t (1t = 1 tonne = 1000 kg)
f. 12.0 mg
1.20 x 10-4 N
19600 N
3. Calculate the gravitational field strength at the surface of each of the following planets:
PLANET
Mercury
Venus
Earth
Mars
Pluto
Mass on the planet’s
surface (kg)
Force of gravity on
this mass (N)
g (N/kg)
57
29
83
453
82
201
247
813
1688
656
3.5
8.5
9.8
3.72
8.0
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Newton’s Law of Universal Gravitation Problems:
Note:
g = 9.80 N/kg
G = 6.67 x 10-11 Nm2/kg2
Mass of Earth: 5.98 x 1024 kg
Radius of Earth = 6.38 x 106 m
4. Why is the gravitational field strength half way up Mount Everest the same as at sea level where g=
9.80 N/kg.
The distance from the center of the earth to that point is not very much different than the distance to the
center of earth alone (radius of the earth is 6.38 x 106 m while Everest itself is 8850 m … now add half
of this height to the radius of the Earth, you get 6.38 x 106 m rounded to three sig. figs.). Since the
height does not add much to the radius value in Newton’s Law of Universal Gravitation, the value of g
does not change significantly. At the top of Everest, along with more precision in the values used, the
value of the gravitational field strength is 9.77 N/kg. Another interesting note is that since the Earth is
not exactly spherical (its radius is larger through the equatorial plane compared to between the poles),
the g value at the equator is less than that at the poles (not much different but measurable).
5. Why is the gravitational field strength at the South Pole less than the field strength at the North
Pole?
Yes, since the Antarctic is actually a continent not just a large sheet of ice and the South Pole has an
elevation of 3700 m … the North Pole is at sea level (just ice flows up there!!). Since the South Pole is
farther from the center of the Earth it must have a lower gravitational field strength.
6. The force of gravity on an astronaut is 600 N at the Earth’s surface. (her mass must be 61.2 kg)
What is the force of gravity on her at each of the following distances from the centre of the Earth,
measured in multiples of the Earth's radius?
a. 2
150 N
c. 10
6N
b. 5
24 N
d. 20
1.5 N
7. The force of gravity on a spacecraft some distance from the Earth is 800 N. What would that force
be if its distance to the Earth's centre were:
a. One – half as great
4 times greater, 3200 N
b. One – third as great
9 times greater, 7200 N
c. One – tenth as great
100 times greater, 8000 N
d. One – quarter as great
16 times greater, 12 800 N
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8. A 20.0 kg object out in space is attracted to the Earth by a force of gravity of 100 N. How fast
will the object accelerate towards the Earth, if it is falling freely?
5.00 m/s2
9. Two of the largest oil tankers in the world, the Batilus and the Bellaya, have masses of 492 000
tonne fully loaded. If they were moored side-by-side, l.0 m apart, their centres would be 64 m
apart. Calculate the force of gravity between them.
3940 N
10. Sirius is the brightest star in the night sky. It has a radius of 2.5 x 10 9 m and a mass of 5.0 x 1031
kg. What is the gravitational force on a 1.0 kg mass at its surface?
534 N
11. Sirius B is a white dwarf star, in orbit around Sirius, with a mass of 2.0 x 10 30 kg (approximately
the mass of the sun), and a radius of 2.4 x l07 m (approximately one-thirtieth of the radius of the
sun).
a. What is the force acting on a l.0 kg mass on the surface of Sirius B?
2.3 x 105 N
b. What is the acceleration due to gravity on the surface of Sirius B?
2.3 x 105 m/s2
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