While a roofer is working on a roof that slants at 37.0 ∘∘ above the horizontal, he accidentally nudges his 92.0 NN toolbox, causing it to s

Question

While a roofer is working on a roof that slants at 37.0 ∘∘ above the horizontal, he accidentally nudges his 92.0 NN toolbox, causing it to start sliding downward, starting from rest. If it starts 4.25 m from the lower edge of the roof, how fast will the toolbox be moving just as it reaches the edge of the roof if the kinetic friction force on it is 22.0 N?

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Amity 5 years 2021-08-01T16:22:46+00:00 1 Answers 601 views 1

Answers ( )

  1. minhkhang
    0
    2021-08-01T16:24:10+00:00
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    Answer:

    The speed is   v =8.17 m/s

    Explanation:

    From the question we are told that

          The angle of slant is  \theta = 37.0^o

           The weight of the toolbox is  W_t = 92.0N

           The mass of the toolbox is m = \frac{92}{9.8} = 9.286kg

           The start point is  d = 4.25m from lower edge of roof

            The kinetic frictional force is  F_f = 22.0N

    Generally the net work done on this tool box can be mathematically represented as

          Net \ work done = Workdone \ due \ to \ Weight + Workdone \ due \ to \ Friction

    The workdone due to weigh is  =    mgsin \theta * d

     The workdone due to friction is  = F_f \ cos\theta * d

    Substituting this into the equation for net workdone  

                     W_{net} = mgsin\theta * d + F_f \ cos \theta *d

          Substituting values

                      W_{net} = 92 * sin (37) * 4.25 + 22 cos (37) * 4.25

                              = 309.98 J

     According to work energy theorem

                 W_{net} = \Delta Kinetic \ Energy

                  W_{net} = \frac{1}{2} m (v - u)^2

    From the question we are told that it started from rest so  u = 0 m/s

                  W_{net} = \frac{1}{2} * m v^2

    Making v the subject

                   v = \sqrt{\frac{2 W_{net}}{m} }

    Substituting value

                  v = \sqrt{\frac{2 * 309.98}{9.286} }

                 v =8.17 m/s

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