Two small boats are towing a ship.Each exerts a force of 3000 N. The angle between the ropes is 60. Find the magnitude of resultant force on ship.(Hint:Apply parallelogram law)
To find the magnitude of the resultant force on the ship, we can use the parallelogram law of vector addition. According to the law, if two forces are represented by two adjacent sides of a parallelogram, then the diagonal of the parallelogram, starting from the common point of those two sides, represents the resultant force.
In this case, the two small boats are exerting a force of 3000 N each, and the angle between the ropes is given as 60 degrees. Let's label the forces as A and B, where A represents the force of the first boat and B represents the force of the second boat.
To apply the parallelogram law, we can construct a parallelogram with sides representing the magnitudes of the two forces, A and B, and the included angle between them.
Now, let's calculate the magnitude of the resultant force on the ship:
Step 1: Draw a diagram representing the parallelogram with sides A and B.
Step 2: Use the given information that each boat exerts a force of 3000 N to label the sides of the parallelogram as 3000 N.
Step 3: Use the given information that the angle between the ropes is 60 degrees to label the included angle.
Step 4: Complete the parallelogram by drawing the diagonal starting from the common point of the two sides.
Step 5: Measure the length of the diagonal, which represents the magnitude of the resultant force on the ship.
Step 6: Calculate the magnitude of the resultant force by using the Law of Cosines.
In this case, the Law of Cosines can be applied to find the length of the diagonal (resultant force):
c^2 = a^2 + b^2 - 2ab * cos(C),
where c represents the length of the diagonal (resultant force), a and b represent the magnitudes of the forces A and B, and C represents the included angle between the forces.
In this case, a = b = 3000 N (as both boats exert the same force), and C = 60 degrees.
Now, substitute the values into the formula and calculate c:
c^2 = (3000 N)^2 + (3000 N)^2 - 2 * (3000 N) * (3000 N) * cos(60°).
c^2 = 9000000 N^2 + 9000000 N^2 - 2 * (3000 N) * (3000 N) * 0.5.
c^2 = 18000000 N^2 - 18000000 N^2.
c^2 = 0.
Notice that the resultant force on the ship is calculated to be zero. This is because the forces A and B are equal in magnitude but act in opposite directions, canceling each other out. Therefore, the magnitude of the resultant force on the ship is zero.