Its a multiple choice. A force of 3N and a force of 4N act on an object at the same time. Which of the following forces cannot be the resultant force on the object? A) 0.5N...B)3.5N...C)4N...D)5N..

Answer 1

From a purely mathematical perspective, 0.5N appears to be the only incorrect answer, How ever, let's view it from a physics perspective.

Let's say an object is acted upon by a force F₁ =4N. At the same time another force F₂ of magnitude = 3N acts on the same object at some unknown angle θº.

When θº is 0, the forces act in the same direction and have a resultant equal to 7N. On the other hand if θº=180, the forces act opposite each other and the resultant is 4-3=1N.

For all values of θº excepting 90°, the magnitude of the component of F₂ along the direction of F₁ must be non-zero.

When F₂ is perpendicular to F₁, the resultant can be determined by the formula R=√(4²+3²)=5N

There is no possible value of θº at which the resultant of F₁ and F₂ will be exactly 4N if F₂ is not 0. This means that not only 0.5N but also 4N is a correct answer for this question.

Answer 2

Forces F₁ = 3N, F₂ = 4N and resultant force R must satisfy Triangle Inequality:

A) F = 05N not satisfy this inequality because 05N < 4N - 3N

B) F = 3.5N satisfy triangle inequality because 3N + 3.5N < 4N and 3N > 4N - 3.5N

C) F = 4N satisfy the triangle inequality because 3N + 4N > 4N and 3N > 4N - 4N

D) F = 5N satisfy tiangle inequality because 3N + 4N > 5N and 3N > 5N - 4N

Answer: Only A) forse 0.5N can't be rsultant of forces 3N and 4N

Answer 3

The rigorous method would be to write a general equation for the sum of the forces, depending on the angle. Since you are given some choices, it's much easier.

Consider some "boundaries":

If the forces are in the same direction, they add: 3 + 4 = 7N

If they are in the opposite direction, they subtract: 4 - 3 = 1N.

For any other combination, the resultant force must be within these limits. Therefore, 0.5N is not possible

Answer 4

Hi Zara Z.,

This is a 2-D vector visualization problem. Draw your 1st vector (let's say the 4N one) on a piece of paper at some orientation. Then your 2nd vector acts in the same plane (it must act in the same plane, for some plane, do you see why?). What sort of region is accessed by swinging the 3N vector from the tip of the 4N one? If you're doing it right, you see that the maximum possible sum is 7N, and the minimum possible is 1 N.

That should enable you to choose, right?

--Cheers, --Mr.. d.