You are working on the plans for an expedition to colonize Mars. In an effort to provide a homey atmosphere for the Mars colonists, the plan is to send a number of grandfather clocks along with the expedition. Each colonist apartment will contain one grandfather clock. You are in charge of designing the clock pendula. The clocks will have a pendulum with a period of T = 2.00 s when the acceleration due to gravity is 9.80 m/s². Your design for the pendulum includes a small object of mass m₁ = 1.65 kg mounted such that its center is at the end of a very light rod, as shown in (a) of the figure. The pivot point is at the upper end of the rod. (a) my L CM X- Y (b) m m₂ CMX m₂ L (a) Determine the required length L for the rod (in m) when the clock is operating with a 2.00 s period on Earth. 0.993
You are working on the plans for an expedition to colonize Mars. In an effort to provide a homey atmosphere for the Mars colonists, the plan is to send a number of grandfather clocks along with the expedition. Each colonist apartment will contain one grandfather clock. You are in charge of designing the clock pendula. The clocks will have a pendulum with a period of T = 2.00 s when the acceleration due to gravity is 9.80 m/s². Your design for the pendulum includes a small object of mass m₁ = 1.65 kg mounted such that its center is at the end of a very light rod, as shown in (a) of the figure. The pivot point is at the upper end of the rod. (a) my L CM X- Y (b) m m₂ CMX m₂ L (a) Determine the required length L for the rod (in m) when the clock is operating with a 2.00 s period on Earth. 0.993
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Transcribed Image Text:You are working on the plans for an expedition to colonize Mars. In an effort to provide a homey atmosphere for the Mars colonists, the plan is to send
a number of grandfather clocks along with the expedition. Each colonist apartment will contain one grandfather clock. You are in charge of designing
the clock pendula. The clocks will have a pendulum with a period of T = 2.00 s when the acceleration due to gravity is 9.80 m/s². Your design for the
pendulum includes a small object of mass m₁ = 1.65 kg mounted such that its center is at the end of a very light rod, as shown in (a) of the figure. The
pivot point is at the upper end of the rod.
(a)
m1
CM X-
L
Use T = 2π
i
m
(b)
m2
CMX-
m1
d
(a) Determine the required length L for the rod (in m) when the clock is operating with a 2.00 s period on Earth.
0.993
L
(b) As shown in (b) of the figure, when the clock is operated on Mars, a small object of mass m₂ can be mounted at a position r that is 29.5% of the
length of the rod from its pivot point. This additional object allows the period of the pendulum to be adjusted when located in different
gravitational fields by altering m₂ while keeping m₁ fixed in both mass and position. The acceleration due to gravity on Mars is 37.6% that on
Earth. Determine the design requirement for the mass m₂ when the clock is operating with a 2.00 s period on Mars. (Entered the required mass
in kg.)
79.9
X
I
to find the period of the physical pendulum. kg
mgd
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