Knocking the bottom of the bottle.

[Petrulis]

Homework Statement

If vitreous bottle is full of water and we strike with a palm from the top to the bottleneck, we can knock out the bottom of the bottle. Why? How to evaluate the force which knocks out the bottom of the bottle?

The Attempt at a Solution

Because water has constant pressure:

Pressure on the top = Force applied / neck area​

=​

Pressure on the bottom = Force bottom/ bottom area​

Force bottom = Force top * bottom area / neck area​

So we knock out the bottom of the bottle because the force gets magnified. Now I need to evaluate "Force top".

Let's say that the mass of the palm is M, and it moves with speed v before strike. The strike takes time moment which is equal to t.

So then this means that:

Force top = M*v/t​

And we get that:

Force bottom = M*v/t * bottom area / neck area​

So is the "Force bottom" evaluated correctly in this problem? Don't I miss anything?

Thanks in advance.

 

[G01]

Its looks pretty good. Your pressure equation is right. Then you find the acceleration and force on the hand, which has to be equal to the force on the top of the bottle:

For the hand:
v_i=-v
v_f=0
t=t

$$v_f=v_i+at$$

so $$a =\frac{-v_i}{t} =\frac{v}{t}$$

Then the force on the hand becomes:

$$F=ma=\frac{mv}{t}$$

Which is equal to the force on the top of the bottle by Newton's Third Law.
Yup looks good to me.

 

[m2003]

I would like to clarify a few points in this scenario. First, the statement that "water has constant pressure" is not entirely accurate. While water does exert pressure on the walls of a container, this pressure can vary depending on the depth of the water and the shape of the container. Additionally, the statement that "the force gets magnified" is not entirely accurate either. The force applied to the bottom of the bottle is not necessarily larger than the force applied to the top, but rather it is distributed over a smaller area, resulting in a higher pressure.

To evaluate the force that knocks out the bottom of the bottle, we need to consider the properties of the bottle and the water, as well as the force applied. Factors such as the thickness and strength of the bottle's glass, the volume and weight of the water, and the force and speed of the strike all play a role in determining the force required to break the bottle's bottom.

In terms of the equation provided, it is important to note that the mass of the palm (M) and the speed of the strike (v) are not the only factors that contribute to the force applied. The angle and surface area of contact between the palm and the bottle also play a significant role. Additionally, the time moment (t) should be replaced with the duration of the impact, as this will affect the force applied.

Overall, it is difficult to accurately evaluate the force required to knock out the bottom of the bottle without specific measurements and experimental data. I would recommend conducting controlled experiments to determine the force needed in this scenario, rather than relying solely on calculations and assumptions.