a cart mass 3kg rolls down a slope. when it reaches the bottom a spring loaded gun fires a 0.5kg ball with horizontal velocity 0.6m/s. find

Question

a cart mass 3kg rolls down a slope. when it reaches the bottom a spring loaded gun fires a 0.5kg ball with horizontal velocity 0.6m/s. find final velocity of the cart

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Thu Hương 4 years 2021-09-04T20:07:15+00:00 1 Answers 21 views 0

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  1. minhkhang
    0
    2021-09-04T20:08:24+00:00
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    Answer:

    the final velocity of the cart is 5.037m/s

    Explanation:

    Using the conservation of energy

    T_a + V_a = T_b + V_b

    T_a = \frac{1}{2} (m_c + m_b)v_a^2

    T_a= \frac{1}{2} (3 + 0.5)(0)^2

    = 0

    V_a = (m_c + m_b)gh_a

    V_a = (3 + 0.5) * 9.81 * 1.24

    = 42.918J

    T _b = \frac{1}{2} (3 + 0.5)v_b^2 \\\\ = 1.75v_b^2

    V_b = (3 + 0.5) * 9.81 * 0\\ = 0

    T_a + V_a = T_b + V_b\\ 0 + 12.918 = 1.75v_b^2 + 0\\v_b = 4.95m/s

    Using the conservation of linear momentum

    (m_c + m_b)v_B = m_cv_c + m_bv_b\\(3 + 0.5) * 4.95 = 3v_c - 0.5v_b\\17.33 = 3v_c - 0.5v_b\\v_b = 6v_c - 34.66 ...............(1)

    Utilizing the relative velocity relation = v_b - v_c\\-0.6 = -v_b - v_c\\v_b = 0.6 - v_c (2)

    equate (1) and (2)

    6v_c - 34.66 = 0.6 - v_c\\7v_c = 35.26\\v_c = 5.037m/s

    the final velocity of the cart is 5.037m/s

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