An Atwood machine consists of two masses hanging from the ends of a rope that passes over a pulley. Assume that the rope and pulley are mass

Question

An Atwood machine consists of two masses hanging from the ends of a rope that passes over a pulley. Assume that the rope and pulley are massless and that there is no friction in the pulley. If the masses have the values m 1 = 17.7 kg m1=17.7 kg and m 2 = 11.1 kg, m2=11.1 kg, find the magnitude of their acceleration a a and the tension T T in the rope. Use g = 9.81 m/s 2 .

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Vân Khánh 4 years 2021-08-21T21:30:00+00:00 2 Answers 21 views 0

Answers ( )

  1. lethu
    0
    2021-08-21T21:31:08+00:00
    Reply

    Answer:

    Explanation:

    m1 = 17.7 kg

    m2 = 11.1 kg

    Let a be the acceleration and T be the tension in the string.

    use Newton’s second law

    m1 g – T = m1 x a ….(1)

    T – m2 g = m2 x a ….. (2)

    Adding both the equations

    (m1 – m2) g = ( m1 + m2 ) x a

    (17.7 – 11.1 ) x 9.8 = (17.7 + 11.1) x a

    64.68 = 28.8 a

    a = 2.25 m/s²

    Put the value of a in equation (1)

    17.7 x 9.8 – T = 17.7 x 2.25

    173.46 – T = 39.825

    T = 133.64 N

  2. kimchi2
    0
    2021-08-21T21:31:23+00:00
    Reply

    Explanation:

    According to Newton’s second law of motion,

                m_{1}g - T = m_{1}a ……… (1)

    and,    T - m_{2}g = m_{2}a ……… (2)

    When we add both equations, (1) and (2) then the expression obtained for “a” is as follows.

                 a = \frac{m_{1} - m_{2}}{m_{1} + m_{2}} \times g

                    = \frac{17.7 - 11.1}{17.7 + 11.1} \times 9.8

                    = \frac{6.6}{28.8} \times 9.8

                    = 2.24 m/s^{2}

    Now, putting the value of “a” in equation (1) then we will calculate the tension as follows.

                  m_{1}g - T = m_{1}a

                  17.7 \times 9.8 - T = 17.7 \times 2.24

                       173.46 – T = 39.648

                           T = 133.812 N

    Thus, we can conclude that the magnitude of their acceleration is 2.24 m/s^{2} and the tension T is 133.812 N in the rope.

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