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Tugboat Ocean
Physics example problem for final exam, need help!?
Two tugboats push an ocean liner sideways toward a pier. The mass of the ship is 50000X10^3 kg. One tugboat pushes the right side(starboard) of the ship near the front (bow) with a force of 4000X10^3 N at an angle of 15 degrees relative to the ships left (portside) direction. The second tugboat pushes the right side of the ship near the rear end (stern) with a force of 4000X10^3 Nat an angle of -15 degrees relative to the left direction. What is the acceleration of the ship? (ignore and effect of friction due to air and water acting on the ship)
There is a sample picture with a large boat lying horizontally on the paper with two small boats on the bottom side pushing it towards the top of the paper.
Thanks for any help.
You'll want to figure out the x-component and y-component of each tug boat's push. Then you'll add up the two x-components with eachother, and then do the same for the y-components.
Fx = Fx1 + Fx2 (Fx = force in x-direction)
Fy = Fy1 + Fy2 (Fy = force in y-direction)
You'll need to do a little trignometry to figure out how much of the force goes into the x-direction, and how much into the y-direction.
Then you can divide both of those sums by the mass of the ship, and you'll have acceleration in the x-direction and acceleration in the y-direction.
Finally, you take those two acceleration components and put them back together as one acceleration. The total acceleration's magnitude will be equal to the square root of the sum of the squares of the x-component acceleration and the y-component acceleration. (I know that sounded confusing. The equation below should make it simpler.)
|a| = sqrt (ax^2 + ay^2)
where |a| is the magnitude of the acceleration,
ax is the acceleration in the x-direction,
ay is the acceleration in the y-direction.
Then you calculate the direction of the final acceleration, and you're done. (Sorry, I don't remember any easy way of doing this. The way I'd give would be more confusing than necessary.)
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Tugboat- Ocean to Ocean
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