 # Easy physics question

OK, at my college we have to do our physics homework online. I hate this, because you submit answers to the system, and if you round wrong, or something, you have an incorrect answer.
Anyways, I was pissed at this problem, because I was 100% sure (as were my friends) of the correct answer:

The force on a 10 kg object increases uniformly from zero to 50N in 6.0s. What is the objects speed at the end of the 6.0 s interval?
That’s the question. I got 30 m/s, using the equation p=mv. Where p is momentum (in kg m/s), v is velocity, and m is mass. So I multiplied the force (50 N) by the time (6 s) because Newtons are kgm/s^2, so multiplying by seconds puts it into units of momentum. I then divided by 10 kg, and got 30 m/s. I got an inncorrect answer. I didn’t ask my professor because I missed the class, so I ask you.

You got it wrong because you multiplied the final force (50 N) by the total time (6.0 s) to get the impulse.

The actual force was
F=50/6 t.

The impulse (change in momentum) was
I= integral of F wrt t, or

I= 50/12 t[sup]2[/sup]

or for this definite integral
I= 50/126[sup]2[/sup]-50/120[sup]2[/sup]

I=150 Ns

assuming that the mass was at rest at t=0 (i.e. momentum=0), then the final speed is 15 m/s.

Are you sure about that actual force number? I would think you could take the average force over time, which would be 25N.

longhorn is correct, but i doubt it is a class with calculus.

average acceleration = (1/2)*(50N/10kg)=(5/2)m/s^2
final speed = avg accel *6 sec = (5/2)*6=15 m/s

-luckie

Yes, I am sure about that actual force. The question states that the force rises uniformly from 0 N to 50 N over 6 seconds. The way to write that in math-speak is:
F=50/6t (for t=0 to t=6).

You could say that the average force was 25 N, but since this is a college level physics class, I assumed some conversance with calculus. The average force happens to be 25 N, but that is only because the force varies linearly with time. The prof was probably trying to test the student’s understanding of a variable force and it’s effect on momentum.

Being out in the real world, I am allowed to use shortcuts, but it is best that the student learn the concept, not the shortcut.

I am a college physics student and great fan of physics and have read every book on Physics I can get my hands on.
::cracks knuckles::
Most scientists would agree with your point of view about learning the concept, not the shortcut. However, the physical CONCEPT in this case is that

“Force varies linearly over time”

Which you then use to say that

The average force is therefore 50/2=25N

You then use this value to compute the speed by your method:

Av. force * time=impulse=mv
therefore
v=(25*6)/10=15m/s

The ‘shortcut’ in this case is to apply a calculus method which, while flashy, does not require understanding of the concept, only of the math.

Disclaimer: I am one of the world’s leading fans of R.P.
Feynman.

Well, thank you guys. I wish I had viewed these replies BEFORE I took that test (just got done.)