39届国际物理竞赛试题IPhO(英文)理论第一题

39th International Physics Olympiad - Hanoi - Vietnam - 2008

Theoretical Problem No. 1

WATER-POWERED RICE-POUNDING MORTAR

A. Introduction

Rice

is

the

main

staple

food

of

most

people

in

Vietnam.

To

make

white

rice

from

paddy rice, one needs separate of the husk (a process called

bran

layer

(

The

hilly

parts

of

northern

Vietnam

are

abundant

with

water

streams, and people living there use water-powered rice-pounding mortar for bran layer

separation. Figure 1 shows one of such mortars., Figure 2 shows how it works.

B. Design and operation

1. Design

.

The rice-pounding mortar shown in Figure 1 has the following parts:

The mortar, basically a wooden container for rice.

The lever, which is a tree trunk with one larger end and one smaller end. It can rotate

around a horizontal axis. A pestle is attached perpendicularly to the lever at the smaller

end. The length of the pestle is such that it touches the rice in the mortar when the lever

lies horizontally. The larger end of the lever is carved hollow to form a bucket. The shape

of the bucket is crucial for the mortar's operation.

2. Modes of operation

The mortar has two modes.

Working mode. In this mode, the mortar goes through an operation cycle illustrated in

Figure 2.

The rice- pounding function comes from the work that is transferred from the pestle to

the rice during stage f) of Figure 2. If, for some reason, the pestle never touches the rice,

we say that the mortar is not working.

Rest mode with the lever lifted up

.

During stage c) of the operation cycle (Figure 2),

as

the

tilt

angle

?

increases,

the

amount

of

water

in

the

bucket

decreases.

At

one

p

articular

moment

in

time,

the

amount

of

water

is

just

enough

to

counterbalance

the

w

eight of the lever. Denote the tilting angle at this instant by

?

. If the lever is kept at

a

ngle

?

and

the

initial

angular

velocity

is

zero,

then

the

lever

will

remain

at

this

position

forever.

This

is

the

rest

mode

with

the

lever

lifted

up.

The

stability

of

this position

depends

on

the

flow

rate

of

water

into

the

bucket,

?

.

If

?

exceeds

some

value

?

,

then this rest mode is stable, and the mortar cannot be in the working

mode.

2

In other words,

is the minimal flow rate for the mortar not to work.

2

?

1

39th International Physics Olympiad - Hanoi - Vietnam - 2008

Theoretical Problem No. 1

Figure 1

A water-powered rice-pounding mortar

2

39th International Physics Olympiad - Hanoi - Vietnam - 2008

Theoretical Problem No. 1

OPERATION CYCLE OF A WATER-POWERED RICE-POUNDING MORTAR

a)

b)

?

1

c)

?

=

?

d)

?

2

?

0

e)

f)

a) At the beginning there is no water in

the bucket, the pestle rests on the mortar.

Water flows into the bucket with a small

rate, but for some time the lever remains

in the horizontal position.

b) At some moment the amount of water

is enough to lift the lever up. Due to

the

tilt, water rushes to the farther side of

the

bucket,

tilting

the

lever

more

quickly.

Water starts to flow out

?

?

?

.

at

1

c

)

As

the

angle

?

increases,

water

starts to flow out. At some particular

tilt

angle,

?

?

?

, the total torque is zero.

d)

?

continues

increasing,

water

continues

to

flow

out

until

no

water

remains in the bucket.

e)

?

keeps

increasing

because

of

inertia.

Due

to

the

shape

of

the

bucket,

water

falls

into

the

bucket

but

immediately

flows

out.

The

inertial motion

of

the

lever

continues

until

?

reaches the maximal

value

?

.

0

f

)

With

no

water

in

the

bucket,

the

weight

of

the

lever

pulls

it

back

to

the

initial

horizontal

position.

The

pestle

Figure 2

gives

the

mortar

(with

rice

inside)

a

pound and a new cycle begins.

3