Finding the initial force from mass, distance, and friction coefficient

[gcharles_42]

Homework Statement

So say there was some object on a Horizontal surface. id there was some force on (not constant, but a hit or something) this object and there was a sliding friction between the surface and the object. How would that factor into the F=ma formula? and what if you are given a mass, and a distance that the object moved (not acceleration), and sliding friction coefficient of course - how would you find the force?

Homework Equations

F=ma

Nuk (N)= Force of Friction

The Attempt at a Solution

Would it be F - F(of friction) = m (a)?

converting that accel to a distance is what is bothering me a lot :/

 

[cepheid]

Hello,

The F in F = ma is always the NET force acting on the object. So, yes, in the beginning, when a force is briefly applied to accelerate the object, the equation would be:

F_applied - F_fric = ma

Once the applied force has ceased, and the object slides to a stop under friction, it is just:

-F_fric = ma

The kinematics equations you probably know are only applicable for constant acceleration. In this situation, the acceleration is not constant, because the net force is not constant with time. For a brief period at the beginning, it includes the initial "hit", and afterwards, it includes only friction. So, you need more information in order to figure things out.

If you knew what final speed the object reached at the end of the initial "hit" (the period during which it was accelerating), and you know the distance over which it traveled *after* reaching that max speed, then this reduces to a standard kinematics problem and you can solve for the decelerating frictional force.

 

[cepheid]

Hmm, ok, this problem is a little more constrained than I first thought. *IF* I assume that the acceleration period (the period of the "hit") was very brief, then I can assume that most of the distance given in the problem was spent decelerating. In the limit where I assume that the object was decelerating over all that distance, then I know the following:

I know v_f = 0

I know the value of 'a' *during the deceleration*, because I know m, which means I know N (it's a horizontal surface), and I know μ_k, which means I know F_fric, and that gives me a.

I know d

From these three things, I can solve for v_i, i.e. how fast must it have been moving just after the "hit" in order for it to require that amount of distance to slow to a stop at that acceleration?

Since I know v_i, I know how much change in momentum, or *impulse*, was delivered by the hit. I can't solve for F_applied (the "hit") from this impulse without knowing over what time interval the hit was delivered. So that's the end of what we can determine.