Determine magnitude and direction of the force exerted on the floor

[cdornz]

Homework Statement

There is a 180 pound basketball player. The coefficient of friction between his right foot and the floor is 0.7. There is no acceleration or sliding in the problem. Determine the magnitude and direction of the force that his right foot is exerting on the floor.

Homework Equations

ƩF=0 (know what since acceleration is zero)
F_friction = (0.7)(F_n) (I know F_n is perpendicular to the interface between the two surfaces and it is not equal to the weight of the object. This is what's stated in my physics book.)
F_{right foot} = -F_gravity - F_n - F_friction

I would then use component forms of the equation, so one for "x" and one for "y"

The Attempt at a Solution

My attempt at this isn't coming out correctly and I honestly have no idea why.

(for the x equation) (0.7)F_ncos0 = F_{right footx}
(for the y equation) 800sin270 + F_nsin90 = F_{right footy}
-800 + F_n = F_{right footy}


I don't know where to go from here, because I'm pretty sure it's already wrong. Any help would be appreciated!

 

[haruspex]

What makes you think there are any horizontal forces involved?

 

[cdornz]

I had assumed when I was given coefficient of friction, that that was involved then. Also if it isn't, the F_{right footx} would be zero and that doesn't make sense.

 

[haruspex]

I had assumed when I was given coefficient of friction, that that was involved then.

That's a dangerous assumption. Good examiners throw in irrelevant information to test for understanding rather than blindly plugging numbers into equations.

Also if it isn't, the F_{right footx} would be zero and that doesn't make sense.

Why not? Would the player be able to stand upright on ice without sliding? What forces would be involved then?

 

[cdornz]

So I had the chance to re-evaluate this problem a little bit and tried solving it from
$\Sigma$F=ma and I know that a=0

so I would have two equations (to get the two components) so one for sine and one for cosine. When I assume that F_n is 180 pounds as well this is what I get:

F_g + F_n + F_{right footx} = ma
180cos270° + 180cos90° + F_{right footx} = 0
0 + 0 + F_{right footx} = 0
F_{right footx} = 0

F_g + F_n + F_{right footy} = ma
180sin270° + 180sin90° + F_{right footy} = 0
-180 + 180 + F_{right footy} = 0
F_{right footy} = 0

But, when I don't assume F_n is 180 pounds, this is what I end up with:

F_g + F_n + F_{right footx} = ma
180cos270° + F_ncos90° + F_{right foodx} = 0
0 + 0 + F_{right footx} = 0
F_{right footx} = 0

F_g + F_n + F_{right footy} = ma
180sin270° + F_nsin90° + F_{right footy} = 0
-180 +F_n + F_{right footy} = 0
F_n + F_{right footy} = 180

In either of these cases, something still doesn't seem right and I'm truly lost as to what component I'm missing.

 

[ap123]

Is there any more to this question that you have left out?
There doesn't seem to be enough information to solve it as it stands.

 

[cdornz]

That was my thought, no there is nothing more to this problem as given. I guess it's possible he left stuff out, but it wouldn't explain how I could solve others in this section.

 

[ap123]

The picture shows a 180 pound basketball player

The picture might help.

 

[cdornz]

Here's the picture.

 

[ap123]

OK, here's my analysis of the situation - I'm not sure if it's completely correct, (maybe someone else can check).

The force that his foot exerts on the floor is equal and opposite to the force that the floor exerts on his foot.
The former is the vector sum of the normal force and the frictional force ( which acts to the right in the picture ).
The normal force is equal to his weight (since there is no acceleration in the vertical direction), and the frictional force = 0.7 * his_weight.
Adding these 2 vectors gives a force of magnitude 220lb, acting at an angle of 55° to the horizontal.
So, the force exerted by his foot is equal and opposite to this.

 

[cdornz]

OK, here's my analysis of the situation - I'm not sure if it's completely correct, (maybe someone else can check).

The force that his foot exerts on the floor is equal and opposite to the force that the floor exerts on his foot.
The former is the vector sum of the normal force and the frictional force ( which acts to the right in the picture ).
The normal force is equal to his weight (since there is no acceleration in the vertical direction), and the frictional force = 0.7 * his_weight.
Adding these 2 vectors gives a force of magnitude 220lb, acting at an angle of 55° to the horizontal.
So, the force exerted by his foot is equal and opposite to this.

So the answer key shows this is the correct answer, but equation wise could you help me break it down?

So you are saying that the arrow (that would be drawn through his right leg) is the sum of the normal force and frictional force? So if normal force is 180 and frictional force is 126, how would that equal 220? I'm just trying to get as accurate of notes as possible so I know how to approach future questions like this.

 

[cdornz]

Wait, nevermind, my bad. I forgot to apply Pythagorean theorem. Thanks for the help!