Download Mass (kg) Radius (m) Moon Mars Earth

Gravitation and Friction Problems
1) Two round apples each have a mass of 200g and a radius of 4cm. If they are touching, what is the gravitational force between them?
m=200g
4cm
m = 200g = 0.200kg
d = 8cm = 0.08m
8cm
The gravitational force between the apples is 4x10­10N.
2﴿ A satellite with a mass of 400kg orbits the Earth at a distance of 36 kilometers. What gravitational force does the satellite exert on the Earth?
400kg
36km=36000m
m1= 400kg
m2= ME= 5.98x1024kg
d=RE+36km = 6.38x106m+36000m = 6.4x106m
RE
ME
The satellite exerts a force of 3.9x103N on the earth (which only is enough to accelerate the earth by 6.5x10­22m/s2).
3) Use the universal gravitation formula and Newton's second law to calculate the free­fall acceleration due to gravity on the surface of
a) the moon
b) Mars
Mass (kg) Radius (m)
c) Earth
Moon
Mars Earth First derive the formula for the free­fall acceleration ag on the surface of a body (e.g. a planet) of mass M and radius R. Consider an object of mass m sitting on the surface. Then by Newton's second law the force of gravity on the object is:
We can also calculate the force of gravity on the object using Universal Gravitation:
Combining our two expressions we get:
divide both sides by m:
(you do not need to memorize the derivation of this formula)
a)
b)
c)
4) A cross country skier is skiing with a constant velocity along level snow. If
the skier weighs 80kg calculate:
a) the normal force of the skier
b) the force of friction on the skier
c) the force the skiier must exert if she wishes to accelerate at 0.5 m/s2.
, and v
FN
a)
Fs
Ff
b)
Fg
c)
5) The gravitational force on a book resting on a level wood table is 20N [down]. A horizontal force of 12N is needed to start the book moving from rest. Calculate .
FN
Ff
FA
Fg
To move the book, we need to apply a force that cancels friction. Assuming that 12N is the minimum force we can apply to move the book, .
6) A force of 450 N is needed to drag a 1000kg box across the floor. Calculate .
FN
Ff
FA
Fg
To move the book, we need to apply a force that cancels friction. Assuming that 450N is the minimum force we can apply to move the book, .