Finding the magnitude of a net force

[elkosp16]

2 problems both with dealing with finding the magnitude of a net force.

1. A gust of wind blows an apple from a tree. As the apple falls, the gravitational force on the apple is 2.25 N downward, and the force of the wind on the apple is 1.05 N to the right. Find the magnitude and direction of the net force on the apple.

2. The wind exerts a force of 452 N north on a sailboat, while the water exerts a force of 325 N west on the sailboat. Find the magnitude and direction of the net force on the sailboat.


I found the direction already.
tan theta = x/y

1. 1.05/2.25 tan-1 = 25 degrees

2. 325/452 tan-1 = 35.7 degrees

So how do you find magnitude?

 

[elkosp16]

never mind. i figured it out. you have to use Pythagorean theorem.

 

[kerimek]

To find the magnitude of a net force in a given situation, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, the net force acts at an angle to the horizontal, so we can use the Pythagorean theorem to calculate its magnitude.

1. Using the given information, we can create a right triangle where the vertical side represents the gravitational force and the horizontal side represents the force of the wind. The net force acts as the hypotenuse of this triangle.

Using the Pythagorean theorem, we can write the equation: (net force)^2 = (gravitational force)^2 + (wind force)^2. Plugging in the values, we get: (net force)^2 = (2.25 N)^2 + (1.05 N)^2. Solving for the net force, we get: net force = √(2.25^2 + 1.05^2) = √5.0625 = 2.25 N.

Therefore, the magnitude of the net force on the apple is 2.25 N and it acts at an angle of 25 degrees to the horizontal.

2. Similarly, for the sailboat, we can create a right triangle where the vertical side represents the force of the water and the horizontal side represents the force of the wind. The net force acts as the hypotenuse of this triangle.

Using the Pythagorean theorem, we can write the equation: (net force)^2 = (water force)^2 + (wind force)^2. Plugging in the values, we get: (net force)^2 = (325 N)^2 + (452 N)^2. Solving for the net force, we get: net force = √(325^2 + 452^2) = √282625 = 532.25 N.

Therefore, the magnitude of the net force on the sailboat is 532.25 N and it acts at an angle of 35.7 degrees to the horizontal.