Question

PLEASE HELP ME ANSWERS THESE:

if you divide momentum measured in N*s(1 N= 1 Kg *m/s^2) by a speed expressed in meters per second, in units will the answer be expressed? (Use the following as necessary: m,s, and kg)

Hooke's famous equation indicates that F = kx, where x is the stretch of a spring from equilibrium and k is the stiffness of the spring measured in kg/s2. Given this, what is the SI unit for F ? (Use the following as necessary: m, kg, and s.)

If you square the impulse expressed in newton-seconds, in what units will the answer be expressed? (Use the following as necessary: N and s.)
units = ?

Answer 1

1). (force) x (time) = (kg-m/s²) x (sec) = kg-m/s

Divide that by speed (m/s), and you're left with kg (mass).

You've just demonstrated than impulse (force x time) has the same units as momentum (mass x speed), and in fact, delivering some impulse does change momentum by the same simple amount.

2). We know that 'x' is a stretch distance, so its unit is 'meter' (length).

If F = kx, and the unit of 'k' is kg/s², then

[F] = (kg/s²) times (meter)

[F] = kg-m/s²

By gosh, that's exactly the combination of units that we call a "Newton".

3). OK. I have no idea what (impulse)² is good for, or whether it has any physical significance, but you want to play with the units. Oh goody ! I love to do that ! So let's do so forthwith:

Impulse = Newton-sec

Impulse = (mass · length / time²) x (time)

Impulse = (mass · length / time) (or mass · speed)

(Impulse²) = mass² · length² / time²

The only interesting thing I can to do with that is

(Impulse²) = (mass² · length) · (acceleration)

Oh wait. That can be further massaged:

Impulse² = (mass · length) · (mass · acceleration)

Impulse² = (mass · length) · (Force)

Impulse² = (mass) · (Force · length)

Impulse² = mass · (work or energy)

Wow ! I still don't know what it's good for, but it shore is interesting.

Answer 2

Explanation:

1. The SI unit of momentum, $p=Newton-second=kgm/s$

We need to divide momentum by the speed.

$\dfrac{p}{v}=\dfrac{kgm/s}{m/s}=kg$

The answer will be expressed in kilogram (kg).

2. Hooke's equation is given by :

F = kx

Unit of k, $k=kg/s^2$

Unit of F, $F=kgm/s^2$

3. Unit of Impulse, $J=Ns$

Unit of square of impulse, $J^2=N^2s^2$

Hence, this is the required solution.