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4 May, 01:13

A small rock with mass 0.12 kg is fastened to a massless string with length 0.80 m to form a pendulum. The pendulum is swinging so as to make a maximum angle of 45 ∘ with the vertical. Air resistance is negligible.

A. What is the speed of the rock when the string passes through the vertical position?

Express your answer using two significant figures.

B. What is the tension in the string when it makes an angle of

45∘ with the vertical?

Express your answer using two significant figures.

C. What is the tension in the string as it passes through the vertical?

Express your answer using two significant figures.

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Answers (1)
  1. 4 May, 03:36
    0
    The answers to the question are

    (a) 2.1 m/s

    (b) 0.83 N

    (c) 1.9 N

    Explanation:

    To solve the question, we list out the varibles

    Length, l of string = 0.8 m

    mass of rock, m = 0.12 kg

    Angle with the verrticakl, θ = 45 °

    a) To find the speed of the rock when the string passes through the vertical position we have

    From the first law of thermodynamics

    Potential energy = kinetic energy

    m*g*l * (1-cosθ) = 1/2*m*v²

    That is v² = 2*g*l * (1-cosθ)

    = 2*9.81*0.8 * (1-cos45) = 4.597

    or v = √4.597 = 2.1 m/s

    (b) The tension in the string when it makes an angle of 45∘ with the vertical is given by

    For balance between Tension and mass of rock is gigen by

    ∑Forces = 0, T - m*g*cosθ = 0

    or T = m*g*cosθ = 0.12*9.81*cos45 = 0.83 N

    c) The tension in the string as it passes through the vertical

    when passing through the vertical we have T - m*g = (m*v²) / r

    or T = m*g + (m*v²) / r = mg (1+2 (1-cosθ)) = 0.981*0.12 (1 + 2 (1-cos45)) = 1.867 N

    = 1.9 N
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