Question

Using the force table, components of a vector can be found experimentally by suspending masses from 2 orthogonal strings which oppose the mass and string representing the vector in question. If 155 g is suspended at 210 degrees, what masses must be suspended at 0 degrees and 90 degrees to balance this force.

I think since they're orthogonal, the could be equal masses to each other. Is this even close to being right? If not, how do I start the process of solving the problem?

Answer 1

Answer: 134.23g at 0° (horizontal) and 77.5g at 90° (vertical).

Step-by-step explanation:

1) Since the mass of 155 g is suspended at 210 degrees, you need to find the components of its weight on the orthogonal coordinate system (0° and 90°).


2) You do that using the trignometric ratios sine and cosine.


Weight is mass × g.

Weight of the object = 155g × g

Angle, α = 210°


Horizontal component (0°)

cosα = horizontal / hypotenuse ⇒ horizontal = hypotenuse × cosα

⇒ horizontal = 155g × g × cos(210°) = - 134.23g × g

Vertical component
sinα = vertical / hypotenuse ⇒ vertical = hypotenuse × sinα
⇒ vertical = 155g × g × sin(210°) = -77.5g × g

3) Conclusion:

Therefore, the masses that must be suspended to balance the forces of the 155g mass are 134.23g at 0° (horizontal) and 77.5g at 90° (vertical).