question archive A boat was tied to a dock using four ropes
A boat was tied to a dock using four ropes
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A boat was tied to a dock using four ropes. The first two are horizontal ropes (forming a right angle with the dock) from the bow and stern of the boat, with a tension of 260 N each. The third rope is tied to the front starboard of the boat and to the rear of the pier, making an angle of 20 ° with the dock, with a tension of 360 N and the fourth rope is tied to the starboard rear of the boat and to the front of the dock, forming an angle of 20 ° with the dock with a tension of 360 N. What is the resulting force applied to the boat?
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tension of two horizontal ropes each, T1=T2=260 N
tension of third rope and fourth rope, T3=T4=360 N
and makes an angle θ= 200 with the dock
thus their horizontal componment is 360cos20
and vertical component is 360sin20
thus the resultant of horizontal forces, TH=T1+T2+T3cosθ+T4cosθ=260+260+360cos20+360cos20=1196.58 N
the resultant in vertical direction, from the conditions provided it is cleat that the components in the vertical direction are opposite in direction and since they are equal in value, ie 360sin20, the force Tv becomes 0
thus the resultant of force on the boat T=sqrt(1196.582+02)=1196.58 N
