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Asked Nov 21, 2019
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Engineering Fundamentals – An Introduction to Engineering

6th Edition – Saeed Moaveni

Chapter 6 Fundamental Dimensions and Units (Pages 157-200)

Question # 6.4 (Page 195)

6.4
Which one of the following equations is dimensionally homogenous? Show your
proof
F=ma
а.
F = m
b.
F(t, - t) — т(V, -и)
с.
F = mV
(V-V,)
(12-)
F = m
е.
where
F = force (N)
m=mass (kg)
a acceleration (m/s2)
V velocity (m/s)
R=radius (m)
ttime (s)
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6.4 Which one of the following equations is dimensionally homogenous? Show your proof F=ma а. F = m b. F(t, - t) — т(V, -и) с. F = mV (V-V,) (12-) F = m е. where F = force (N) m=mass (kg) a acceleration (m/s2) V velocity (m/s) R=radius (m) ttime (s)

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Step 1

a)

Provide the dimensions in the equation F=ma as shown below.

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F = ma N-kg x m/s2 N N ma is dimensionally homogeneous Hence, F

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Step 2

b)

Provide the dimensions in the equation F=mV2/R as shown below.

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V 2 = m F (m/s)' N kg x N kg xm/s N N V2 is dimensionally homogeneous R Hence, F m

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Step 3

c)

Provide the dimensions in the equation F(t2-t1)=m(V2-V1) as shown bel...

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F(t-1) m(V -) s kg xm/s Ns kg xm/s X X Ns Ns Hence, F(4m(V, - V) is dimensionally homogeneous

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