Find F2 on a particle given velocity vector and F1 vector

[MrMoose]

Homework Statement

While two forces act on it, a particle is to move continuously with v = (3 m/s)i - (4 m/s)j. One of the forces is F1 = (2N)i + (-6N)j. What is the other force?

Homework Equations

My main problem is with the verbiage, "move continuously". Does this suggest constant acceleration? If yes, then I would reference an equation for motion with constant acceleration such as:

v^2 = v02 + 2a(x - x0)

However, there's too many unknowns to use this equation (and other equations for motion). I don't know time, distance, initial velocity, or acceleration.

The Attempt at a Solution

My thought process:
1. Find accelerations (a)i and (a)j using equation for motion and given velocity vector (It would have to be in terms of variables since there's several unknowns)
2. Find total forces (F)i and (F)j on the particle using F = ma (again, it would have to be in terms of 'm' since I don't know the mass). Unknowns cancel out in the end?
3. Take the difference between the total force vector F and F1 to determine F2

This seems like a very convoluted path to take and I'm pretty sure it's not correct. What am I missing from the initial problem statement? I feel like there's more information there that I'm not getting.

The answer is F2 = (-2N)i+(6N)j

This confuses me. How can you have an object in motion if two equal and opposite forces are acting on it? Shouldn't it be stationary? It makes me think that this is more of a conceptual problem than a calculation intensive problem. Thanks for your help in advance - MrMoose

 

[arildno]

"To move continuously" means, at all times, to move with the velocity given.
Thus, the velocity is a CONSTANT, the acceleration=0

 

[arildno]

" How can you have an object in motion if two equal and opposite forces are acting on it? Shouldn't it be stationary?"
What does Newton's first law state?

 

[Princu]

Hello Mr.Moose..
The problem is really easy.
The particle moves continuously with v = (3 m/s)i - (4 m/s)j means that the velocity of the particle(both components) do not change with time.For this,acceleration of particle in both the directions should be zero..
i.e.Force in both the directions must be zero. It is known that F1 = (2N)i + (-6N)j so F2 must be opposite to it for net force on the particle to be zero.Hence F2 = (-2N)i+(6N)j

 

[arildno]

"My thought process:
1. Find accelerations (a)i and (a)j using equation for motion and given velocity vector (It would have to be in terms of variables since there's several unknowns)
2. Find total forces (F)i and (F)j on the particle using F = ma (again, it would have to be in terms of 'm' since I don't know the mass). Unknowns cancel out in the end?
3. Take the difference between the total force vector F and F1 to determine F2"

A perfectly fine thought process in the GENERAL case, if you were given a velocity profile v(t), and the mass of the object. In this case, you do not NEED the mass, for the velocity is a CONSTANT, so that the unknown mass vanishes in F=m*a

 

[MrMoose]

Wow, thank you very much for the detailed replies. So let me summarize to make sure I understand.

To "move continuously" suggests the particle is not accelerating (a = 0) and the velocity is constant.

We know that F = F1 + F2 = ma = m * 0 = 0

Therefor F2 = -F1 = (-2N)i+(6N)j

So, in this problem, it's actually irrelevant that the velocity vector is (3 m/s)i - (4 m/s)j. All that matters is that velocity is constant.

I understand this computationally, but I'm still getting hung up on the conceptual portion of it. Arildno, you asked me to take a second look at Newton's First Law:

"When viewed in an inertial reference frame, an object either is at rest or moves at a constant velocity, unless acted upon by an external force."

I understand that the particle in question is at constant velocity, but I'm trying to understand the reference frame. Was the particle set in motion by a force outside the frame of reference of this question? I imagine a stationary particle outside the frame of reference with forces F1 and F2 acting on it set in motion by a third force that isn't considered in this question. Is that a good way of looking at it? I'm still puzzled at how the particle is in motion.

 

[arildno]

It belongs to the PRE-history of the system you're looking at that it accelerated up to its present state of motion.

You are just zooming onto a time interval in which it has a constant, non-zero velocity, and don't care how it got that velocity in the first place.

 

[MrMoose]

Nice, thanks! That wraps it up.