Question

A stationary nucleus has nucleon number A.
The nucleus decays by emitting a proton with speed v to form a new nucleus with speed u. The
new nucleus and the proton move away from one another in opposite directions.
what is the equation which gives v in terms of A and u?

Answer 1

Hello! So what have you got so far?

Answer 2

Hello ! hmmm ... nothing special :P

Answer 3

^_^ Well, what do you think you do to start? Conservation of energy? Newton's laws? Conservation of momentum?

Answer 4

conservation of momentum ... first the .. momentum is zero .. then .... the story starts

Answer 5

and oh, what a grand story it is!! ^^

What are the velocities of the nucleus and the ejected proton?

Answer 6

I guess a picture is in order, first off.

Answer 7

So the u is in the positive direction and the v is in the negative direction in the picture;

\[v_n = u
\\ v_p = -v\]

Answer 8

yes

Answer 9

So what next?

Answer 10

the answer is v = (A – 1)u ....... but i am missing some step i guess .......

Answer 11

Only 1 teeny step - can you set up the right hand side of the conservation of momentum?

\[\cancel{p_i}^0 = p_f\]

Answer 12

\[0=A \times v - u\]

Answer 13

The nucleus is what has velocity u - the proton has velocity v.

Also, what does the problem say about the original mass of the nucleus?

Answer 14

the original mass of the nucleus is not given ....

Answer 15

It is, actually - they just hid it.

Saying "having a nucleon number A" is how they gave the mass. They're using atomic mas units instead of kilograms or grams or something. They're sneaky.

In the atomic mass unit system, a proton = 1 .

So if the nucleus mass starts out at A, then loses 1 proton, what does that make the mass?

Answer 16

~proton = 1 amu

Answer 17

~nucleus mass starts out at mass A amu

Answer 18

but still i cannot achieve the answer ..........

Answer 19

so
\[m_n=(A-1)amu
\\ m_p=1amu\]

\[p_i=p_f\]
\[0=m_nu-m_pv\]
\[0=((A-1)amu \ )u - (1 \ amu) \ v\]
\[(1 \ amu) \ v = ((A-1)amu)u\]
\[v=(A-1)u\]

Answer 20

Do you get how I defined the mass?

Answer 21

so the mass of the nucleus is A-1 ? ...... which means 1 proton is lost ..

Answer 22

yes yes

- this is a really weird problem

Answer 23

true ..

Answer 24

A strong wind of speed 33 m s–1 blows against a wall. The density of the air is 1.2 kg m–3. The wall
has an area of 12 m2 at right angles to the wind velocity. The air has its speed reduced to zero
when it hits the wall.
What is the approximate force exerted by the air on the wall?