How Does Impulse Affect Momentum in Physics?

[bona0002]

Hey guys,

Alright, I feel like this is super easy, but for some reason, I'm not getting the right answer. Could you guys point out my flaw? There are (one can say) three coequal theories of motion for a single particle: Newton's second law, stating that the total force on an object causes its acceleration; the work–kinetic energy theorem, stating that the total work on an object causes its change in kinetic energy; and the impulse–momentum theorem, stating that the total impulse on an object causes its change in momentum. In this problem, you compare predictions of the three theories in one particular case. A 3.50-kg object has velocity 7.00j m/s. Then, a constant net force 8.0i N acts on the object for 4.50 s.
(a) Calculate the object's final velocity, using the impulse–momentum theorem.

Process:
The impulse-momentum theorem says that Δp = I.
With that said, we obviously need to find the v_f_, so I would speculate that the impulse-momentum theorem can be broken down to say mv_f_ - mv_i_ = I. Solving for v_f_, the expression becomes ((I + mv_i_)/m).
Now, I = F * Δt (because F is a constant force). Plugging in values, (8.o N) * (4.5s) = (36.0 N*s).
Therefore, plugging in the final value of impulse, v_f_ = ((36.0 N*s + (3.50 kg)(7.00 m/s))/(3.50 kg) = 17.3 m/s

So, with all that said, where am I going wrong?

Thanks!

 

[TSny]

You haven't taken into account the fact that the force is not in the same direction as the initial velocity.

 

[bona0002]

Taking that into account then, may I inquire how that changes the setup of my problem-solving process? Unfortunately, I'm not seeing it right now.

 

[TSny]

It doesn't change the general process. Momentum and impulse are vector quantities. So, the impulse-momentum theorem is $\vec{I} = \Delta\vec{p}= m\vec{v}_f-m\vec{v}_i$. When you substitute for $\vec{I}$ and $\vec{v}_i$, be sure to include the unit vectors $\hat{i}$ or $\hat{j}$.

 

[bona0002]

So, if I'm understanding this correctly, my substitution did yield the "correct" answer, it's just that the answer needs to be expressed in i and j hat notation?

 

[TSny]

No, your answer is incorrect because you didn't include the unit vectors during the calculation. It's not a matter of just putting in a unit vector at the end.

 

[bona0002]

Ok, I'll reword it with the unit vectors in mind, and see what I come out with.

 

[TSny]

OK. Note, for example, the difference between 2 + 3 and 2$\hat{i}$ + 3$\hat{j}$. The first summation yields 5, but the second summation gives something entirely different.

 

[bona0002]

Ok, the answer worked out. That was a stupid mistake on my part. Thank you for the help!