Show that the force needed to keep a mass m in a circular path of radius r with period T is 4 π 2 m r T 2 .

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Show that the force needed to keep a mass m in a circular path of radius r with period T is             4              π        2            m      r              T      2        .

kriteria0b1 · Accepted Answer

To show: The force needed to keep a mass m in a circular path of radius r with period T is   F  =            4              π        2            m      r              T      2        .Explanation of SolutionCalculation:Show the expression of net force as follows:      F          n      e      t        =  m  a    =            m              v        2              r  Here, r is circular path of radius, v is constant speed, m is the object mass, and a is the acceleration.The period of motion is the circumference,  C  =            2      π      r        v  Express the time period of motion of the circumference as follows:  T  =            2      π      r        v   (2)Modify Equation (2).  v  =            2      π      r        T  Substitute             2      π      r        T   for v in Equation (1).  F  =            m      (                        2          π          r                T                    )        2              r      =      m    r    (            2      π      r        T        )    2      =      m    r    (            4              π        2                    r        2                    T      2        )    =            4              π        2            m      r              T      2      The force needed to keep a mass m in a circular path of radius r with period T is   F  =            4              π        2            m      r              T      2

Show that the force needed to keep a mass m in a circular path of radius r with period T is 4 pi^2mr/T^2.

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