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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 = 1.82 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) (b) my CM X- L m mo CMX- m1 d 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. (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 that is 30.5% 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.) kg

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 = 1.82 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) (b) my CM X- L m mo CMX- m1 d 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. (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 that is 30.5% 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.) kg

Physics for Scientists and Engineers: Foundations and Connections
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter1: Getting Started
Section: Chapter Questions
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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 = 1.82 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) (b) m1 CM X- m m₂ CMX kg my 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. Y (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 that is 30.5% 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.)
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 = 1.82 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) (b) m1 CM X- m m₂ CMX kg my 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. Y (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 that is 30.5% 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.)
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