A thin rod of mass M and length l hangs from a pivot at its upper end. A ball of clay of mass m and of horizontal velocity v strikes the low

Question

A thin rod of mass M and length l hangs from a pivot at its upper end. A ball of clay of mass m and of horizontal velocity v strikes the lower end at right angles andremains stuck (total inelastic collision).

Required:
How high will the rod swing after this collision?

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Calantha 1 year 2021-08-06T13:31:45+00:00 1 Answers 59 views 0

Answers ( )

    0
    2021-08-06T13:33:26+00:00

    Answer:

     P = 2923.89 W

    Explanation:

    Power is

         P = F v

    so This exercise will solve them in parts using the conservation of momentum and then using the conservation of energy

    To use the conservation of the momentum we must define a system, formed by the bodies, so that the forces during the collision have internal forces and the moment is conserved

    initial instant, before the crash

            p₀ = m v

    final instant. Right after the crash

           [tex]p_{f}[/tex] = (M + m) v₂

           p₀ =p_{f}

           m v = (M + m) v₂

           v₂ = m / (m + M) v

    this is the speed with which two come out, now we can apply the conservation of energy to the system formed by the two bodies together

    Starting point. Lower

            Em = K = ½ (M + m) v²

    Final point. Highest point

            Em = U = (M + m) g h

            Eo₀ = [tex]Em_{f}[/tex]

             ½ (M + m) v2 = (M + m) g h

              h = 1/2 v2 / g

             

              h = ½ [m / (m + M) v] 2 / g

             

              h = 1/2 (m / m + M) 2 / g we must calculate the force, let’s use Newton’s second law, let’s set a coordinate system with a parallel axis flat and the other axis (y) perpendicular to the plane

    X Axis

             Fe – Wₓ = 0

             F = Wₓ

    Y Axis

             N – [tex]W_{y}[/tex] = 0

    let’s use trigonometry for the components of the weight

             sin 6 = Wₓ / W

             cos 6 = [tex]W_{y}[/tex] / W

             Wx = W sin 6

             W_{y}= W cos 6

              F = mg cos 6

              F = 75 9.8 cos 6

              F = 730.97 N

    let’s calculate the power

            P = F v

            P = 730.97 4.0

            P = 2923.89 W

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