two forces, one of 35 pounds and the other 62 pounds, act upon the same object. The angle between these forces is 25 degrees. Find the magnitude of the resultant force.
To find the magnitude of the resultant force, you can use the concept of vector addition.
1. First, split the forces into their horizontal and vertical components.
The horizontal component of the 35-pound force can be found by multiplying it by the cosine of the angle between the force and the x-axis. Since the angle is 25 degrees, the horizontal component of the 35-pound force is 35 * cos(25°).
The vertical component of the 35-pound force can be found by multiplying it by the sine of the angle between the force and the x-axis. So the vertical component of the 35-pound force is 35 * sin(25°).
Similarly, find the horizontal and vertical components of the 62-pound force using the same method.
2. Add up the horizontal components and the vertical components separately.
Add up the horizontal components of the two forces to find the horizontal component of the resultant force.
Add up the vertical components of the two forces to find the vertical component of the resultant force.
3. Use the Pythagorean theorem to find the magnitude of the resultant force.
The magnitude of the resultant force can be found by taking the square root of the sum of the squares of its horizontal and vertical components.
In mathematical terms, the magnitude of the resultant force (Fresultant) can be calculated as Fresultant = √(horizontal component^2 + vertical component^2).
Substitute the values of the horizontal and vertical components calculated in step 2 into this equation to find the magnitude of the resultant force.