Say you want to make a sling by swinging a mass M of 2.3 kg in a horizontal circle of radius 0.034 m, using a string of length 0.034 m. You

Question

Say you want to make a sling by swinging a mass M of 2.3 kg in a horizontal circle of radius 0.034 m, using a string of length 0.034 m. You wish the mass to have a kinetic energy of 13.0 Joules when released. How strong will the string need to be

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Sigridomena 2 weeks 2021-09-02T20:05:23+00:00 1 Answers 0 views 0

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    2021-09-02T20:06:42+00:00

    Answer:

    T = 764.41 N

    Explanation:

    In this case the tension of the string is determined by the centripetal force. The formula to calculate the centripetal force is given by:

    F_c=m\frac{v^2}{r}  (1)

    m: mass object = 2.3 kg

    r: radius of the circular orbit = 0.034 m

    v: tangential speed of the object

    However, it is necessary to calculate the velocity v first. To find v you use the formula for the kinetic energy:

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

    You have the value of the kinetic energy (13.0 J), then, you replace the values of K and m, and solve for v^2:

    v^2=\frac{2K}{m}=\frac{2(13.0J)}{2.3kg}=11.3\frac{m^2}{s^2}

    you replace this value of v in the equation (1). Also, you replace the values of r and m:

    F_c=(2.3kg)(\frac{11.3m^2/s^2}{0.034})=764.41N

    hence, the tension in the string must be T =  Fc = 764.41 N

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