# Newton second law involving a gallon of water

1. Nov 9, 2011

1. The problem statement, all variables and given/known data
a box filled of water is over at the beginning of a incline plane of 30 degree, it has a mass of 1 kg,from the bottom of the plane to the top is 10m, the gallon is pushed with a force of 10N to the top, and the gallon is leaking 0.01kg per second

what is the final velocity?
2. Relevant equations

f=ma

3. The attempt at a solution
analyzing this problem each since the force doesnt change, the mass decrease each second so the acceleration increase each second. i really dont know how to solve this problem when involving a gallon of water leaking.

Last edited: Nov 10, 2011
2. Nov 9, 2011

### sandy.bridge

Only when the mass remains constant does Newton's Second Law of motion reduce to
$$\vec{F}=m\vec{a}$$
When dealing with variable mass, use
$$\vec{F}=\frac{d}{dt}(m\vec{v})$$

3. Nov 9, 2011

Last edited: Nov 9, 2011
4. Nov 9, 2011

so it means the mass is constant, it only changes the velocity

5. Nov 9, 2011

### sandy.bridge

No, the mass is not constant. It is changing with time. Also, did you copy the question down fully, and properly?

6. Nov 9, 2011

well if you dont understand my question u can ask me

7. Nov 9, 2011

as far i understand time is changing as well as mass and velocity

8. Nov 9, 2011

### Ray Vickson

This equation is known to be incorrect in general, although it is true in some cases. Correct classical variable-mass equations of motion were finally well established in the 1990s! Before that, many incorrect results appeared in the published literature. Google 'variable-mass dynamics' for relevant papers.

RGV

9. Nov 9, 2011

so... this is harder now, can u help me?

10. Nov 10, 2011

### PeterO

A couple of questions:

Is this a gallon of water or a kilgram of water? A litre of water has a mass of 1 kg.
If this is a gallon, is this a US gallon [8 lb] or an imperial gallon [10 lb],

EDIT: I ask about which gallon as I don't know where you are posting from.

Last edited: Nov 10, 2011
11. Nov 10, 2011

### sandy.bridge

Interesting to know.. Especially considering this was in my Calculus textbook from January 2009.

12. Nov 10, 2011

actually is not really a gallon of water....is just a box or tank filled with water which leak every second.

13. Nov 10, 2011

### Liquidxlax

i'm pretty sure that the volume isn't important just the change in mass

14. Nov 14, 2011

### PeterO

If the box was not leaking, it would take only about 2 seconds to reach the top, arriving with a velocity of about 10 m/s.

In two seconds, the mass will have reduced from 1.00 kg to 0.98 kg - a very small change, so the final velocity won't be much bigger.
Since data was given to one specific figure only, the answer should be 1 x 101 regardless.

15. Nov 14, 2011