What do the intermediate steps (2) and (3) mean in 1 J = 1 N m = 1 kg m² s⁻²?

[richard9678]

Homework Statement

I cannot understand what is written in my textbook.

Homework Equations

i.e:

1 J = 1 N m (I get that) ........(1)

= 1 Kg m s^-2 x m ......(2)

= 1 Kg m² s^-2...(3)

The Attempt at a Solution

If I push a 1 Kg mass (in space) at an acceleration of 9.8 m s^-2) then the Force will be 1 N. And if I push the mass 1 m, that is 1 N m of work done.

What are expressions (2) and (3) saying?

 

[TSny]

1 J = 1 N m (I get that) ........(1)

= 1 Kg m s^-2 x m ......(2)

= 1 Kg m² s^-2...(3)If I push a 1 Kg mass at an acceleration of 9.8 m s^-2 then the Force will be 1 N.

A force of 1 N will accelerate a 1 kg mass at 1 m/s².

And if I push the mass 1 m, that is 1 N m of work done.

What are expressions (2) and (3) saying?

They are just showing how the Joule can be expressed in terms of the three base SI units: kg, m, s.

 

[PhanthomJay]

Homework Statement

I cannot understand what is written in my textbook.

Homework Equations

i.e:

1 J = 1 N m (I get that) ........(1)

= 1 Kg m s^-2 x m ......(2)

= 1 Kg m² s^-2...(3)

The Attempt at a Solution

If I push a 1 Kg mass at an acceleration of 9.8 m s^-2) then the Force will be 1 N.

it will be 9.8 kg.m/sec^2, which is called 9.8 N , since a Newton is defined as a kg.m/sec^2.

And if I push the mass 1 m, that is 1 N m of work done.

9.8 N.m of work done, or 9.8 kg.m^2/sec^2 in longhand form.

What are expressions (2) and (3) saying?

Same thing, in SI basic units of mass, length, and time. Force is a derived quantity.

 

[richard9678]

Aah, I was making a mistake with the definition of the Newton. I was (for some reason) thinking that the definition of the Newton had something to do with Earth's gravity. Of course, gravity exerts a force of 9.8 Newtons on a 1 Kg mass, not 1 Newton.

(1) is talking about a unit called Newton metres.

(2) is talking about a unit called?

(3) is talking about a unit called?

 

[TSny]

(2) and (3) are combinations of base SI units. You can call (3) a "kilogram meter-squared per second-squared"

 

[richard9678]

Having thought about this, these are my thoughts:

The definition of the Newton is the force it takes to accelerate a 1Kg mass (in space, outside of a gravitational field) at 1 m/s/s.

So, really, whatever work done that it takes to move that 1 Kg, can be expressed in terms of Kg per metre of movement - of a body in space. If the mass is 2 Kg, then work done doubles. Move a 1 Kg mass at an acceleration of 1 m/s/s, 1 metre and work done is 1 J.

You can also express the work done in terms of Kg per second of the movement of a body in space. Double the time, and work done doubles. Move a 1 Kg mass at an acceleration of 1 m/s/s for 1 second and work done is 1 joule.

Of course, here were talking about a mass hanging in space. And referring to mass, time, distance, acceleration.

If we get away from mass in space, and units associated with that situation, we may talk about Newton metres.

A force of 1 Newton moving anything, whatever it's mass, no matter how long it takes, 1 metre, equals 1 J of work done. There will be no acceleration if the force remains constant. And it is this Newton metre measure, that is really an equivalent to the other measures.

My 2 cents. I think I solved my problem.