A meter stick has a mass of 0.21 kg and balances at its center. When a small chain is suspended from one end, the balance point moves 14.0 c

Question

A meter stick has a mass of 0.21 kg and balances at its center. When a small chain is suspended from one end, the balance point moves 14.0 cm toward the end with the chain. Determine the mass of the chain.

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Orla Orla 3 years 2021-08-06T00:14:42+00:00 2 Answers 87 views 0

Answers ( )

  1. phucdien
    0
    2021-08-06T00:15:47+00:00
    Reply

    Answer:

    The mass is  M_n = 0.047kg

    Explanation:

    From the question we are told that

             The mass of the meter stick  is M_c = 0.21kg

              The distance by which the balance point moves d = 14.0 \ cm

    Before the movement of the balance point  was at the middle of the meter stick i.e at the 50 cm mark

     Mathematically the weight of the meter stick would be

                              W = M_c g  

       where g is acceleration due to gravity with a value of   9.8m/s^2

                             W = 0.12 * 9.8

                                 =1.176N

    Now when the small chain is suspended from one end and the system reach equilibrium the net torque is zero and this implies that

          The moment of force of the meter stick = moment of force of the necklace

                                   W * 14 = W_n * (50 - 14)

     Where W_n is the weight of the necklace

         Substituting values and making W_n the subject we have

                              W_n = \frac{1.176*14}{36}

                                     =0.457N

       Mathematically the weight of the chain is  

                      W_n = M_n * g

    Substituting values and making M_n the subject

                    M_n = \frac{W_n}{g}

                            =\frac{0.457}{9.8}

                             M_n = 0.047kg

                                   

  2. mocmien2
    0
    2021-08-06T00:15:48+00:00
    Reply

    Answer:

    0.082 kg

    Explanation:

    The center of the meter stick = 50 cm.

    When a small chain is place at one end, the balance point is moved 14 cm towards the end with the chain.

    The new balance point = 50-14 = 36 cm

    Using the principle of moment,

    Sum of clockwise moment = sum of anti clockwise moment.

    W(36-0) = W'(50-36)……………… Equation 1

    Where W = weight of the chain, W’ = weight of the meter stick

    36W = 14W’

    make W the subject of the equation

    W = 14W’/36…………………….. Equation 2

    Given: W’ = m’g, where m’ = mass of the meter stick, m’ = 0.21 kg

    W’ = 0.21(9.8) = 2.058 N

    Substitute into equation 2

    W = 14(2.058)/36

    W = 0.8 N

    But

    W = mg,

    Where m =  mass of the chain.

    m = W/g

    m = 0.8/9.8

    m = 0.082 kg.

    Hence the mass of the chain = 0.082 kg

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