Um corpo de massa m= 2,0Kg é lançado horizontalmente, de uma altura h= 125m, com velocidade de módulo Vo =10m/s, como mostra a figura. Desp

Question

Um corpo de massa m= 2,0Kg é lançado horizontalmente, de uma altura h= 125m, com velocidade de módulo Vo =10m/s, como mostra a figura. Desprezando a resistência do ar e adotando g= 10m/s2 , determine: a) A energia mecânica total do corpo; b) A energia cinética do corpo a meia altura em relação ao solo; c) O tempo gasto até que o corpo atinja o solo; d) O alcance do movimento.

in progress 0
King 5 months 2021-09-02T09:33:53+00:00 1 Answers 2 views 0

Answers ( )

    0
    2021-09-02T09:35:27+00:00

    Answer:

    A) E = 2550 J

    B) K = 1325 J

    C) t = 5,05 s

    Explanation:

    A) The total mechanical energy is given by the sum of the gravitational potential energy and the kinetic energy of the body:

    E=U+K=mgh+\frac{1}{2}mv^2  (1)

    m: mass of the body = 2,0 kg

    g: gravitational acceleration = 9,8 m/s^2

    h: height = 125 m

    v: initial velocity of the body = 10 m/s

    You replace the values of all variables h, m, g and v in the equation (1):

    E=(2,0kg)(9,8m/s^2)(125m)+\frac{1}{2}(2,0kg)(10m/s)^2=2550\ J

    the total mechanical energy is 2550 J

    B) The kinetic  energy of the corp, when it is at a height of h/2 is given by:

    K=\frac{1}{2}mv^2

    where

    v=\sqrt{(v_x)^2+(v_y)^2}

    The x component of the velocity is constant in the complete trajectory, which is the initial velocity, that is, vo = vx

    The y component is given by:

    v_y^2=v_{oy}^2+2gy

    voy: vertical initial velocity = 0m/s

    y: height = h/2 = 125/2 = 62.5 m

    v_y=\sqrt{2g\frac{h}{2}}=\sqrt{2(9.8m/s^2)(62.5m)}=35m/s

    Then, you can calculate the velocity of the body and next, you can calculate the kinetic energy:

    v=\sqrt{(10m/s)^2+(35m/s)^2}=36,40\frac{m}{s}\\\\K=\frac{1}{2}(2,0kg)(36,40m/s)^2=1325\ J

    C) The time that body takes in all its trajectory is:

    t=\sqrt{\frac{2h}{g}}=\sqrt{\frac{2(125m)}{9,8m/s^2}}=5,05s

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )