# Can you find the applied force with just the initial and final velocties?

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1. Oct 19, 2014

### glenohumeral13

1. The problem statement, all variables and given/known data
I'm trying to create a problem for my physics standards that is hard. I gave myself a ball being pushed down a carpeted decline at 24° from the horizontal. The balls starts with an initial velocity of 1 m/s and ends the 6 meter decline at 5 m/s. I want to find the applied force on the ball.

2. Relevant equations
Perhaps "1/2vf2 = g*hi"?

3. The attempt at a solution
Found a stalemate because I don't want to give the mass, or else the problem is too easy. So, I can't use "Fg = m*ag".

2. Oct 19, 2014

### haruspex

Do you know about dimensional analysis? This would tell you that force involves a mass dimension, so you cannot calculate a force from only distance and time dimensions.
(Why a ball? Wouldn't a ball roll?)

3. Oct 19, 2014

### NTW

I assume that you mean the rolling friction force of the ball with the carpeted incline... (?)

4. Oct 19, 2014

### glenohumeral13

Okay. Thanks.
Yeah, it probably should have been a block.

5. Oct 19, 2014

### glenohumeral13

Could I find that with the given information?

6. Oct 19, 2014

### Staff: Mentor

No. The problem is unsolvable - in the same way the question "I am in a car and accelerate. It is 2 pm. Find the mass of the car" is not solvable.

7. Oct 19, 2014

### NTW

I'm not sure... Let's see... The final velocity of the ball will be the same in free fall or rolling with no resistance along the incline. That velocity would be v = SQR (2 * 9,81 * 6 m * sin 24º) = 6,91 m/s. You state that there is an extra initial velocity of 1 m/s, so we would have a total of 7,91 m/s.

But 5 m/s is mentioned in the problem as final velocity. Thus, there is a braking force. It could come from rolling resistance and from rotational kinetic energy acquired by the ball during its run... Rolling resistance is a function of the mass of the ball, g, the angle and a coefficient mu. Rotational kinetic energy is a function of the angular velocity w, itself a funcion of v and the ball's radius r, and of the moment of inertia of a sphere 2/5 * m* r^2

Mass is not given. It might cancel away, I'm not sure, but the problem could perhaps be solved 'by energies', deriving the solution also in terms of the unknown magnitudes, maybe m (if it doesn't cancel away), a coefficient of rolling resistance mu, and the ball's radius r...

That, in case it can be solved at all... I am myself a solver of easy problems only...

8. Oct 19, 2014

### haruspex

As I wrote in post #2, dimensional analysis proves there is not enough information. You have to be given a quantity with a mass dimension - could be mass, force, energy, momentum..., but distances times and accelerations by themselves cannot do it.

9. Oct 19, 2014

### glenohumeral13

Haha. Okay. Thanks everybody. I'll just do something with μk and the coefficient then.