Two children on the beach are pulling on an inner tube. One exerts a force of 45 N[N]. The other exerts a force of 60N[SW]. What is the net force acting on the tube
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To find the net force acting on the tube, we need to combine the two forces exerted by the children. The net force is the resultant force when all the forces acting on an object are added together. Since we are given the magnitudes and directions of the forces, we can use vector addition to find the net force.
First, let's break down the force exerted by the second child into its horizontal and vertical components. The force of 60N[SW] has a magnitude of 60N and a direction of southwest (45 degrees below the west direction).
To find the horizontal component, we need to find the side length adjacent to the 45-degree angle in the southwest direction. By using trigonometry (specifically cosine), we can find that the horizontal component is 60N * cos(45) ≈ 60N * 0.707 ≈ 42.4N.
To find the vertical component, we need to find the side length opposite to the 45-degree angle in the southwest direction. By using trigonometry (specifically sine), we can find that the vertical component is 60N * sin(45) ≈ 60N * 0.707 ≈ 42.4N.
Now, we can add the horizontal and vertical components of the forces separately.
Horizontal component: The first child exerts a force of 45N[N], which means 45N acting in the north direction. Since there are no other horizontal forces mentioned, the horizontal component of the net force is simply the first child's force: 45N.
Vertical component: The first child's force does not have a vertical component (since it is acting only in the north direction). Therefore, the vertical component of the net force is the vertical component of the second child's force, which is -42.4N (opposite to the upwards direction).
Now we can find the net force by combining the horizontal and vertical components using vector addition. The net force in the horizontal direction is 45N, and in the vertical direction, it is -42.4N. To find the net force magnitude and direction, we can use the Pythagorean theorem and trigonometry.
Net force magnitude: Magnitude of the net force = sqrt((45N)^2 + (-42.4N)^2) ≈ sqrt(2025N^2 + 1793.76N^2) ≈ sqrt(3818.76N^2) ≈ 61.86N.
Net force direction: To find the direction of the net force, we can use trigonometry (specifically the arctan function) to find the angle it makes with the north direction. The angle is given by arctan(42.4N/45N) ≈ 45.9 degrees.
Therefore, the net force acting on the tube is approximately 61.86N at an angle of 45.9 degrees above the north direction.