One student is pushing on a chair with a force of 260.6 N directed at an angle of 30 degrees above horizontal while a second student pushes on the same side of the chair with a force of 21.0 N at an angle of 15 degrees below horizontal. What is the magnitude, in N, of the sum of these forces?

Question

One student is pushing on a chair with a force of 260.6 N directed at an angle of 30 degrees above horizontal while a second student pushes on the same side of the chair with a force of 21.0 N at an angle of 15 degrees below horizontal. What is the magnitude, in N, of the sum of these forces?

how do i go about solving this question?

Answer 1

add them.

using i,j coordinates

F= 260.6(sin30 j+ cos30 i)+ 21(sin-15 j+ cos 15 i)

then combine terms, and finally, use the right triangle..

Fnet= sqrt (forcei^2+forcej^2)

Answer 2

What do you mean by

Fnet= sqrt (forcei^2+forcej^2)

fnet= 380^2?

Answer 3

To solve this question, you need to break down the forces into their horizontal and vertical components and then find the resultant force in both the horizontal and vertical directions. Finally, you can use the Pythagorean theorem to find the magnitude (overall strength) of the sum of these forces.

Here's a step-by-step guide:

1. Resolve the force of the first student (260.6 N at 30 degrees) into horizontal and vertical components. To do this, you can use trigonometry. The horizontal component (F1x) can be found using the equation F1x = F1 * cos(theta1), where F1 is the force and theta1 is the angle of 30 degrees. Similarly, the vertical component (F1y) can be found using the equation F1y = F1 * sin(theta1).

2. Resolve the force of the second student (21.0 N at 15 degrees) into horizontal and vertical components using the same equations as in step 1. Let's call these components F2x and F2y.

3. Calculate the horizontal component of the resultant force (Frx) by adding the horizontal components of both students' forces: Frx = F1x + F2x.

4. Calculate the vertical component of the resultant force (Fry) by adding the vertical components of both students' forces: Fry = F1y + F2y.

5. Use the Pythagorean theorem: The magnitude of the resultant force (Fr) can be found using the equation Fr = sqrt(Frx^2 + Fry^2).

6. Substitute the respective values from steps 1, 2, 3, and 4 into step 5 to get the magnitude of the sum of the forces.

Following these steps, you should be able to find the magnitude of the sum of these forces.