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 = 2.16 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)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 r that is 31.5% 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% of 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.)
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
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 = 2.16 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)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 r that is 31.5% 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% of 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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