# Homework Help: Simple force vector question

1. Sep 23, 2011

### Hockey07

1. The problem statement, all variables and given/known data

This was an exam question that one of my friends recently had.

Two horizontal forces act on a 32.5kg object. The first force has a magnitude of 210N and points in the direction 40.0 degrees East of North. The second force has a magnitude of 350N and points in the direction 20.0 degrees North of West.

What is the magnitude of the acceleration of the object?

2. Relevant equations

$\Sigma F = ma$

3. The attempt at a solution

We know how to solve this problem, but the correct answer on the exam was 10.5 $\frac{m}{s^{2}}$

The issue with this problem is that we believe it's very vaguely worded.

We solved the problem by doing:

$\Sigma Fx = -350cos(20) + 210sin(40) = 32.5a_{x}$
$\Sigma Fy = 350sin(20) + 210cos(40) - 32.5(9.81) = 32.5a_{y}$

Then the magnitude of the acceleration would be the square root of the sum of the squares of the acceleration components.

Neglecting gravity and using $\Sigma Fy = 350sin(20) + 210cos(40) = 32.5a_{y}$ yields the correct answer on the exam. Neither of us thought to assume that gravity just disappears (because why would it?)

What do you think - vague question or not?

2. Sep 23, 2011

### PeterO

Perhaps you both though the object was "floating" in space. The questioner, and I, assumed the mass was on a flat, frictionless surface.

3. Sep 23, 2011

### Xyius

The problem doesn't explicitly say where the object is but I also assumed it was on a flat friction-less surface. Gravity would, in this case, be cancelled out by the normal force of the surface. This is one of those problems where you should clarify with the teacher as you are taking the tests to rule out any confusion.

4. Sep 24, 2011

### Hockey07

I've taken both Physics and Dynamics and I don't think I've ever had to assume that an object is sitting on a surface. It's always been stated in the question or it's obvious (like a moving car, which clearly is on a road). This question immediately struck me as being a non-obvious situation, and I initially solved it incorrectly.

Additionally, the question explicitly states that there are two horizontal forces, which is not true. There are horizontal components, but the forces are not pointing in the horizontal direction.

5. Sep 24, 2011

### PeterO

Sorry, But directions like North, East and West apply to a horizontal plane. I can't see that you want it clearer than that.

Perhaps you are thinking North is Up, South is Down, East is Right and West is Left - like as if you were looking at a map pinned to a wall?? And thus that East and West are the only horizontal directions?????

6. Sep 24, 2011

### Hockey07

hor·i·zon·tal   [hawr-uh-zon-tl, hor-]
1. at right angles to the vertical; parallel to level ground.
2. flat or level: a horizontal position.

http://dictionary.reference.com/browse/horizontal

I understand the directions just fine. I'm not asking what direction they're pointing in. I'm telling you that the wording is flawed. Read below.

Problem statement: "Two horizontal forces act..."
Me: "They are not strictly horizontal forces."

These forces are not at a right angle to the vertical, nor are they parallel to the ground. They don't fit the definition of horizontal. They are forces causing horizontal motion, and they do have horizontal components. I completely understand that! The problem statement says the forces themselves are horizontal... as in they have NO vertical component (hence the definition horizontal = at right angle to the vertical). They clearly have components in both the vertical and horizontal directions (and no component in the direction perpendicular to that plane since it's a 2D problem).

Also, by not explicitly stating that it's on a flat frictionless surface, you have to assume something that completely changes the problem. There's no indication that it would be resting on any surface. You have to guess that. It's not a fundamental assumption in order to solve the problem (like a fluid mechanics problem where you may assume a fluid is incompressible).

The wording is what bothers me. I know how to do the problem correctly, but the wording just is not clear.

Last edited: Sep 24, 2011
7. Sep 24, 2011

### PeterO

If the questioner says "Two horizontal forces act ..." and you think that says "They are not strictly horizontal forces .." I am not surprised you found the problem confusing.

I still think you are confusing North with vertical, and only if I assume you think that can I find any logic in what you are saying.

8. Sep 24, 2011

### SammyS

Staff Emeritus
A solution in which has gravitational force acting in the Southerly direction seems to be indefensible. How can you possibly argue that the problem as presented is that ambiguous?

9. Sep 25, 2011

### PeterO

I am not the one finding any ambiguity!