A dart gun consists of a horizontal spring with k = 52 Newtons/m that is compressed 43 the gun is cocked. What is the initial accelera

Question

A dart gun consists of a horizontal spring with k = 52 Newtons/m that is compressed 43
the gun is cocked. What is the initial acceleration of a 75-g dart when the gun is fired?

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Kim Chi 3 months 2021-08-12T23:48:17+00:00 1 Answers 1 views 0

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    2021-08-12T23:49:35+00:00

    Answer:

    299 m/s^2

    Explanation:

    When a spring is compressed, the force exerted by the spring is given by:

    F=kx

    where

    k is the spring constant

    x is the compression of the spring

    In this problem we have:

    k = 52 N/m is the spring constant

    x = 43 cm = 0.43 m is the compression

    Therefore, the force exerted by the spring on the dart is

    F=(52)(0.43)=22.4 N

    Now we can apply Newton’ second law of motion to calculate the acceleration of the dart:

    F=ma

    where

    F = 22.4 N is the force exerted on the dart by the spring

    m = 75 g = 0.075 kg is the mass of the dart

    a is its acceleration

    Solving for a,

    a=\frac{F}{m}=\frac{22.4}{0.075}=299 m/s^2

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