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Forces 2 dimensions: How far have the tugboats moved the log

  1. May 6, 2016 #1
    1. The problem statement, all variables and given/known data
    Two tugboats are pulling on a large log, as shown in the following diagram. The log has a mass of 250 kg and is initially at rest. How far have the tugboats moved the log after 10 s?
    upload_2016-5-6_20-36-9.png

    2. Relevant equations
    c2 = a2 + b2 - 2abcosC

    c = (a2 + b2- 2abcosC)1/2

    upload_2016-5-4_15-22-57-png.100276.png

    upload_2016-5-6_20-50-52.png



    3. The attempt at a solution

    c2 = a2 + b2 - 2abcosC

    c = (a2 + b2- 2abcosC)1/2

    c = [(400 N)2 + (800 N)2 - 2 (400 N) x (800 N) cos 150°]1/2

    c= 1164 N

    sinβ/800 N = sin 150°/ 1164 N

    β = 20°

    (To determine the angle for Fnet, subtract 10° from 20°, which equals 10°, as this results in the angle needed to describe the direction for Fnet.)

    Fnet = 1164 N [W 10° N]

    a = 1164 N [W 10° N] / 250 kg

    = 4.66 m/s2 [W 10° N]

    Δd = ½ 4.66 m/s2[W 10° N] x (10 s)2

    Δd = 233 m [W 10° N]

    The tugboats have moved the log 233 m [W 10° N] after 10 seconds.

    Is this correct?
     
  2. jcsd
  3. May 6, 2016 #2

    haruspex

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    Looks good.
     
  4. May 6, 2016 #3
    Ok thanks :)
     
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