Simple physics question

[fullset]

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The arrows shown below represent all the force vectors
that are applied to a single point. Which of the following
could NOT be true of the point? (Note: sin 150° = 0.5;
cos 150 = -root3/2



A. The point is moving at a constant velocity.
B. The point is not moving.
C. The point is accelerating at a constant rate.
D. The point is not accelerating.

The correct (or incorrect) answer is C. I figured out the answer because choices a, b, and d are essentially the same thing. But I would like to know the scientific solutions.

All replies are appreciated.

 

[dingyibvs]

You find if the forces cancel each other out. The easiest way is to rotate the image a bit so that one of the forces line up with an axis(X or Y). Let's line the 2F vector with the Y axis so that the two exactly coincide.

Now, the sqrt(3)F vector will have an X and a Y component, let's consider the X component first. It's in a 30-60-90 triangle, so its X component would be sqrt(3)F/2. Next, calculate the X component of the F vector. It's also in a 30-60-90 triangle, and its X component would be sqrt(3)F/2, which cancels out the X component of the sqrt(3)F vector, since they point in opposite directions.

Similarly, the Y component of the sqrt(3)F vector would be sqrt(3)*sqrt(3)/2 * F = 3F/2. The Y component of the F vector would be F/2. Adding the two together, since they're pointing in the same direction, would give you 3F/2 + F/2 = 2F, which exactly cancels out the 2F vector.

You end up with no net force on the point, and therefore C must be the only false statement and thus the right answer.

 

[fullset]

Thanks a lot. Really helped me!

 

[FrkyBgStok]

you are using examkrackers i see. that one messed me up at first too.