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Represent each of the following units as a combination of primitive
dimensions where M=mass, L=length, T=time

PLS show work

Watt

Newton

Horsepower

Sagot :

mistressofdark

Some important and basic points:

Unit of time is second (s).

Unit of mass is kilogram (kg).

Unit of distance/displacement is meter (m).

P.S. Displacement and distance are nearly same things, their unit is same.

Speed/velocity = distance/time

So, its unit is m/s.

Acceleration = (final velocity-initial velocity)/time.

So, its unit is m/s² or m.s^-2

We know from the formula that,

Force = mass × acceleration

=> F = ma

Putting units:

Newton = kg.m/s² or kg.m.s^-2 _____(1)

Putting dimensions:

Newton = M.L.T^-2

________________________

We know from the formula that,

Work = force × displacement

=> W = Fs

Putting units:

Joule = Newton.m

=> Joule = kg.m.s^-2.m [from (1)]

=> Joule = kg.m².s^-2 ______(2)

Putting dimensions:

Joule = M.L².T^-2

________________________

We know from the formula that,

Power = work/time

Putting units:

Watt = joule/s

=> Watt = kg.m².s^-2/s [from (2)]

=> Watt = kg.m².s^-3 ______(3)

Putting dimensions:

Watt = M.L².T^-3

________________________

We know from the formula that,

Horsepower = 746 watt

=> Horsepower = 746kg.m².s^-3 [from (3)]

Putting dimensions:

Horsepower = 746M.L².T^-3

Hope it helps!!

abidemiokin

The dimension of Watt, Newton and horsepower are ML²T⁻³, MLT⁻² and ML²T⁻³ respectively

Units and dimension

Units are measure of a quantity. Dimensions are derived from the units. Gi

Force = mass × acceleration

For Newton:

Another representation for unit of Newton is  kg.m/s². Writing in terms of the dimension

Newton = MLT⁻²

For Watts;

The unit of Watt is also kg.m².s⁻²/s which is equivalent to  kg.m².s⁻³

In terms of dimension

Dimension of Watt = ML²T⁻³

For Horse power:

The unit of horse power is  kg.m².s⁻³

Dimension of horsepower = ML²T⁻³

Learn more on units and dimension here: https://brainly.com/question/28464

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