A bullet with mass 5.35 g is fired horizontally into a 2.174-kg block attached to a horizontal spring. The spring has a constant 6.17 102 N/

Question

A bullet with mass 5.35 g is fired horizontally into a 2.174-kg block attached to a horizontal spring. The spring has a constant 6.17 102 N/m and reaches a maximum compression of 6.34 cm.
(a) Find the initial speed of the bullet-block system.
(b) Find the speed of the bullet.

in progress 0
Ngọc Hoa 4 years 2021-07-13T10:58:37+00:00 1 Answers 37 views 0

Answers ( )

  1. Farah
    0
    2021-07-13T10:59:44+00:00
    Reply

    Answer:

    a)V=1.067\: m/s

    b)v=434.65\: m/s  

    Explanation:

    a)

    Using the conservation of energy between the moment when the bullet hit the block and the maximum compression of the spring.

    \frac{1}{2}MV^{2}=\frac{1}{2}k\Delta x^{2}

    Where:

    • M is the bullet-block mass (0.00535 kg + 2.174 kg = 2.17935 kg)
    • V is the speed of the system
    • k is the spring constant (6.17*10² N/m)
    • Δx is the compression of the spring (0.0634 m)

    Then, let’s find the initial speed of the bullet-block system.

    V^{2}=\frac{k\Delta x^{2}}{M}

    V=\sqrt{\frac{6.17*10^{2}*0.0634^{2}}{2.17935}}

    V=1.067\: m/s

    b)

    Using the conservation of momentum we can find the velocity of the bullet.

    mv=MV

    v=\frac{MV}{m}

    v=\frac{2.17935*1.067}{0.00535}

    v=434.65\: m/s  

    I hope it helps you!

                 

     

Leave an answer

Browse

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