Question

What is the magnitude of the resultant force, in newtons, acting on an object that has two forces acting in the same direction having magnitudes of 15 newtons and 25 newtons and a third force acting perpendicular to the first two having a magnitude of 30 newtons?

Answer 1

To find the magnitude of the resultant force, we can use the Pythagorean theorem and the trigonometric ratios.

First, we need to find the horizontal and vertical components of the two forces acting in the same direction:

Horizontal component = 15 N + 25 N = 40 N

Vertical component = 0 N (since the forces are in the same direction)

Next, we need to find the horizontal and vertical components of the third force acting perpendicular to the first two:

Horizontal component = 0 N (since the force is perpendicular to the other forces)

Vertical component = 30 N

Now, we can find the horizontal and vertical components of the resultant force:

Horizontal component = 40 N + 0 N = 40 N

Vertical component = 0 N + 30 N = 30 N

Using the Pythagorean theorem, we can find the magnitude of the resultant force:

Resultant force = sqrt((40 N)^2 + (30 N)^2)

Resultant force = sqrt(1600 N^2 + 900 N^2)

Resultant force = sqrt(2500 N^2)

Resultant force = 50 N

Therefore, the magnitude of the resultant force is 50 newtons.

Answer 2

Imagining that the forces form a right triangle (since the 3rd force is acting perpendicularly) then the resultant force can simply be calculated using the hypotenuse formula:

c^2 = a^2 + b^2

Where a and b is equivalent to:

a = 15 N + 25 N = 40 N

b = 30 N

Therefore the resultant force is then calculated:

c^2 = (40 N)^2 + (30 N)^2

c^2 = 1,600 + 900

c^2 = 2,500

c = 50 N