Chapter 1, Problem 71P

Another unit is kgf, which is a force unit used mostly in Europe, and is defined as kp (kilopond). Explain the difference between kilopond (kp = kgf) and kilopound (10³ lbf) from force units and write the unity conversion factor between them. The density of water at 4°C is = 1000 kg/m³. Express this density value in units of $kp\cdot m^{-4}\cdot s^2$ .

To determine

The difference between the kilopond and kilopound.

The unity conversion factor between kilopound and kilopound.

The density of water in $kp\cdot {\text{s}}^{\text{2}}/m^4.$

Answer to Problem 71P

The difference between the kilopond and kilo pound is shown in the table (1).

The unity conversion factor between kilopound and kilopound is:

  $1\text{kgf}=2.204\text{kip}$.

The density value in $\text{kip}\cdot {\text{m}}^{\text{-4}}\cdot {\text{s}}^{\text{2}}$ is $2.204\text{kip}\cdot {\text{m}}^{-4}\cdot {\text{s}}^{\text{2}}$.

Explanation of Solution

Table (1) shows the difference between the pound mass and pound force.

kilopond $\left(\text{kgf}\right)$	kilopound $\left(\text{kip}\right)$
In presence of gravity D, the force applied on the body on unit mass having acceleration due to gravity $g$ can be expressed in $\text{kgf}$ .	Killopound represents the weight or force unit. Kilopound can also be written as $\text{kip}$ .
The expression for kilopond can be written as $\begin{array}{c}F=1\text{kg}\times \text{9}\text{.81}\text{m}/{\text{s}}^{\text{2}}\\ =9.81\text{kg}\cdot \text{m}/{\text{s}}^{\text{2}}\left(\frac{1\text{N}}{1\text{kg}\cdot \text{m}/{\text{s}}^{\text{2}}}\right)\\ =9.81\text{N}\end{array}$ Here $1\text{kgf}=\text{9}\text{.81}\text{N}$	Write the expression for the kilo pound in $\text{lbf}$ . $1\text{kip}=1\text{000}\text{lbf}$ Write the expression for the kilo pound in terms of Newton. $1\text{kip}=\text{4448}\text{.22}\text{N}$
Kilopond can be expressed in the kilo pound as $1\text{kgf}=2.204\text{kip}$	Kilo pound can be expressed in kilo pond as $1\text{kip}=0.\text{453}\text{kgf}$

Table-(1)

Write the expression for the conversion factor between kilopond and kilopound

  $1\text{kgf}=2.204\text{kip}$

Write the expression for density.

  $\rho =\frac{m}{V}$

Here, the density of the substance is $\rho$ and the mass of the substance is $m$ and the volume of the substance is $V$.

Write the expression for volume in $\text{kg}/{\text{m}}^{\text{3}}.$

  $\rho =\frac{1kg}{1{\text{m}}^{\text{3}}}$...... (I)

Calculation:

Multiply Equation (I) by $\text{m}/{\text{s}}^{\text{2}}$ in denominator as well as nominator.

  $\rho =\frac{1kg\left(\text{m}/{\text{s}}^{\text{2}}\right)}{1{\text{m}}^{\text{3}}\left(\text{m}/{\text{s}}^{\text{2}}\right)}$...... (II) Substitute $1\text{kgf}$ for $kg\left(\text{m}/{\text{s}}^{\text{2}}\right)$ in Equation (II).

  $\rho =\frac{1\text{kgf}}{1{\text{m}}^{\text{3}}\left(\text{m}/{\text{s}}^{\text{2}}\right)}$...... (III)

Substitute $2.204\text{kip}$ for $1\text{kgf}$ in Equation (III).

  $\begin{array}{l}\rho =\frac{2.204\text{kip}}{1{\text{m}}^{\text{3}}\left(\text{m}/{\text{s}}^{\text{2}}\right)}\\ \rho =2.204\text{kip}\cdot {\text{m}}^{-4}\cdot {\text{s}}^{\text{2}}\end{array}$

Conclusion:

The difference between the kilopond and kilopound is shown in the table (1).

The unity conversion factor between kilopound and kilopound is $1\text{kgf}=2.204\text{kip}$.

The density value in $\text{kip}\cdot {\text{m}}^{\text{-4}}\cdot {\text{s}}^{\text{2}}$ is $2.204\text{kip}\cdot {\text{m}}^{-4}\cdot {\text{s}}^{\text{2}}$.