A body with a mass of 7.41 kg moves along the x ‑axis, influenced by a conservative force F ( x ) . → F ( x ) = A x 3 ^ x where A = − 4 N m

Question

A body with a mass of 7.41 kg moves along the x ‑axis, influenced by a conservative force F ( x ) . → F ( x ) = A x 3 ^ x where A = − 4 N m 3 When the body is at position x i = 2.05 m, it is moving with a speed of v i = 6.51 m / s. What is the body’s speed when it is at position x f = − 2.65 m?

in progress 0
Jezebel 5 months 2021-08-09T07:19:45+00:00 1 Answers 2 views 0

Answers ( )

    0
    2021-08-09T07:20:54+00:00

    Answer:

    7.136 m/s

    Explanation:

    We are given that

    Mass =m=7.41 kg

    F(x)=Ax^3 hat{x}

    Where A=-4 N/m^3

    x_i=2.05 m

    u=v_i=6.51 m/s

    We have to find the speed of body when it is position x_f=-2.65 m

    According to work energy theorem

    [tex]\frac{1}{2}mv^2-\frac{1}{2}mu^2=\int_{2.05}^{-2.65}-4x^3 dx

    \frac{1}{2}m(v^2-u^2)=-[x^4]^{2.05}_{-2.65}

    \frac{1}{2}(7.41)(v^2-(6.51)^2)=-((2.05)^4-(2.65)^2)

    \frac{1}{2}(7.41)(v^2-42.3801)=31.6545

    v^2-42.3801=\frac{31.6545\times 2}{7.41}

    v^2-42.3801=8.5437

    v^2=8.5437+42.3801=

    v=\sqrt{8.5437+42.3801}

    v=7.136 m/s

Leave an answer

Browse

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