Engineering Fundamentals
Engineering Fundamentals
6th Edition
ISBN: 9780357112144
Author: Saeed Moaveni
Publisher: MISC PUBS
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Chapter 6, Problem 13P

(a)

To determine

Find the given equation is dimensionally homogenous or not.

(a)

Expert Solution
Check Mark

Answer to Problem 13P

The given equation is dimensionally homogenous and it is proved.

Explanation of Solution

Given data:

The equation is,

F(x2x1)=12mV2212mV12 (1)

Here,

F is the force in N,

m is the mass in kg,

x1,x2 is the distance in m, and

V1,V2 is the velocity in ms,

Formula used:

The SI unit expression in terms of base units as follows,

N=kgms2

Calculation:

Find the given equation is dimensionally homogenous or not.

Substitute the units N for F, kg for m, m for x1, m for x2, ms for V1 and ms for V2 in equation (1).

N(mm)=12(kg)(ms)212(kg)(ms)2Nm=12(kgm2s2kgm2s2)Nm=12kgm2s2 (2)

Here,

12 is constant (unitless).

Equation (2) becomes,

Nm=(kgms2)m (3)

Substitute the unit kgms2 for N in equation (3).

Nm=Nm (4)

From equation (4), Left-hand side (LHS) is equal to Right-hand side (RHS). Thus, the given equation is dimensionally homogenous and it is proved.

Conclusion:

Hence, the given equation is dimensionally homogenous and it is proved.

(b)

To determine

Find the given equation is dimensionally homogenous or not.

(b)

Expert Solution
Check Mark

Answer to Problem 13P

The given equation is not dimensionally homogenous and it is proved.

Explanation of Solution

Given data:

The equation is,

F=12mV2212mV12 (5)

Here,

F is the force in N,

m is the mass in kg, and

V1,V2 is the velocity in ms.

Formula used:

The SI unit expression in terms of base units as follows,

N=kgms2

Calculation:

Find the given equation is dimensionally homogenous or not.

Substitute the units N for F, kg for m, ms for V1 and ms for V2 in equation (5).

N=12(kg)(ms)212(kg)(ms)2N=12(kgm2s2kgm2s2)N=12kgm2s2 (6)

Here,

12 is constant (unitless).

Equation (6) becomes,

N=(kgms2)m (7)

Substitute the unit kgms2 for N in equation (7).

N=Nm (8)

From equation (8), Left-hand side (LHS) is not equal to Right-hand side (RHS). Thus, the given equation is not dimensionally homogenous and it is proved.

Conclusion:

Hence, the given equation is not dimensionally homogenous and it is proved.

(c)

To determine

Find the given equation is dimensionally homogenous or not.

(c)

Expert Solution
Check Mark

Answer to Problem 13P

The given equation is not dimensionally homogenous and it is proved.

Explanation of Solution

Given data:

The equation is,

F(V2V1)=12mx2212mx12 (9)

Here,

F is the force in N,

m is the mass in kg,

x1,x2 is the distance in m, and

V1,V2 is the velocity in ms,

Formula used:

The SI unit expression in terms of base units as follows,

N=kgms2

Calculation:

Find the given equation is dimensionally homogenous or not.

Substitute the units N for F, kg for m, m for x1, m for x2, ms for V1 and ms for V2 in equation (9).

N(msms)=12(kg)(m)212(kg)(m)2Nms=12(kgm2kgm2)Nms=12kgm2 (10)

Here,

12 is constant (unitless).

Equation (10) becomes,

Nms=kgm2 (11)

Substitute the unit kgms2 for N in equation (11).

(kgms2)ms=kgm2kgm2s3=kgm2 (12)

From equation (12), Left-hand side (LHS) is not equal to Right-hand side (RHS). Thus, the given equation is not dimensionally homogenous and it is proved.

Conclusion:

Hence, the given equation is not dimensionally homogenous and it is proved.

(d)

To determine

Find the given equation is dimensionally homogenous or not.

(d)

Expert Solution
Check Mark

Answer to Problem 13P

The given equation is dimensionally homogenous and it is proved.

Explanation of Solution

Given data:

The equation is,

F(t2t1)=mV2mV1 (13)

Here,

F is the force in N,

m is the mass in kg,

t1,t2 is the time in s, and

V1,V2 is the velocity in ms,

Formula used:

The SI unit expression in terms of base units as follows,

N=kgms2

Calculation:

Find the given equation is dimensionally homogenous or not.

Substitute the units N for F, kg for m, s for t1, s for t2, ms for V1 and ms for V2 in equation (13).

N(ss)=(kg)(ms)(kg)(ms)Ns=kgmskgmsNs=kgms (14)

Substitute the unit kgms2 for N in equation (14).

Ns=kgms(kgms2)s=kgms

kgms=kgms (15)

From equation (15), Left-hand side (LHS) is equal to Right-hand side (RHS). Thus, the given equation is dimensionally homogenous and it is proved.

Conclusion:

Hence, the given equation is dimensionally homogenous and it is proved.

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Chapter 6 Solutions

Engineering Fundamentals

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