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Physics

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To move a large crate across a rough floor, you push on it with a force at an angle of 21 below the horizontal, as shown in the figure.
Find the acceleration of the crate if the applied force is 400 , the mass of the crate is 32 and the coefficient of kinetic friction is 0.31.

  • Physics - ,

    I assume you are pushing downward, the angle is confusing.

    If you are pushing downward, some of that is pressing downward increasing fn

    fn=mg+Fsin21
    fhorizontal=Fcos21

    horizontal force-friction= ma

    F*cos21-mu*(mg+Fsin21)=m(400)

    solve for F. You did notput units in the statement, you need to check them

  • Physics - ,

    Fc = mg = 32kg * 9.8Nkg = 313.6N = Force of crate.

    Fp = mg*sin(0) = 313.6sin(0) = 0 N =
    Force parallel to the plane = Fh.

    Fv = mg*cos(0) + Fap*sin21,
    Fv = 313.6cos(0) + 400sin21 = 456.9N =
    Force perpendicular to plane. Fap = Applied force.

    Ff = u*Fv = 0.31 * 456.9 = 141.7N =
    Force of friction.

    Fn = Fap*cos21 - Fp - Ff,
    Fn = 400cos21 - 0 - 141.7 = 231.7N =
    Net force.

    a = Fn / m = 231.7 / 32 = 7.2m/s^2.

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