What is the net work done on the boat by the two locomotives?

AI Thread Summary
The discussion revolves around calculating the net work done on a boat being pulled by two locomotives through a canal. The initial calculations involved using the tension in the cables and the length of the canal, but a mistake was made in determining the work done due to the angle of tension. Participants clarified that the correct approach requires multiplying by the cosine of the angle to find the effective force in the direction of travel. The correct net work was calculated to be approximately 1.91E8 J, emphasizing the importance of correctly resolving the tension components. Overall, the conversation highlights common pitfalls in physics calculations involving angles and forces.
leezak
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The drawing shows a boat being pulled by two locomotives through a canal of length 2.39 km. The tension in each cable is 4.17E4 N, and = 16.7°. What is the net work done on the boat by the two locomotives?

first I used W=fd... i multiplied 4.17E4 * 2 = 8.34E4 to get the total tension in each string. then to get the total work i multiplied that by 2390 (m) = 1.99E8... i divided that by two to get the work in each string = 9.97E7... then i realized that would be the tension in each string if the string was perpendicular to the boat so i found the hypotenuse using cos(16.7)=9.97E7/H that gave me 1.04E8. in order to get the net work i multiplied that by two becuase there are two strings and i got 2.08E8 J. that answer is wrong and i can't figure out why... can someone help please?! thanks!
 
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Your approach seems correct. You may have a math mistake somewhere. I got 1.91E8 J.
 
leezak said:
... so i found the hypotenuse using cos(16.7)=9.97E7/H that gave me 1.04E8. ...
Looks like you divided by cos(16.7) instead of multiplying by it :smile:

I got the same as Hotvette.
 
but if i am trying to find the hypotenuse of the triangle... shouldn't i divide instead of multiply?
 
The tension on the cable represents the hypotenuse. What you want is the component in the direction of travel.
 
oh thank you!
 

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