Chapter 3, Problem 21A

Different materials rest on a table.

a. From greatest to least, rank them by how much they resist being set into motion.

b. From greatest to least, rank them by weight.

c. From greatest to least, rank them by the support (normal) force the table exerts on them.

To determine

Ranking of the materials from greatest to least by how much they resist being set into motion.

Answer to Problem 21A

Ranking of materials by how much they resist is given as: $f_B>f_A>f_C>f_D$ .

Explanation of Solution

Given:

Mass of sand, $m_A=12\text{ kg}$

Mass of iron, $m_B=15\text{ kg}$

Mass of water, $m_C=10\text{ kg}$

Mass of pillow, $m_D=2\text{ kg}$

Formula used:

Force of friction is given by:

  $f=\mu mg$

Calculation:

According to the given formula, the force of friction is directly proportional to the mass, because $\mu$ and $g$ are constants. So,

  $f\propto m$

Hence, the resistance of the materials being set into motion is ranked according to the masses:

  $m_B>m_A>m_C>m_D$

So, the final result will be:

  $f_B>f_A>f_C>f_D$

Conclusion:

Ranking of materials by how much they resist is given as: $f_B>f_A>f_C>f_D$ .

To determine

Ranking of materials by their weight.

Answer to Problem 21A

The ranking of materials according to their weight is: $W_B>W_A>W_C>W_D$ .

Explanation of Solution

Given:

Mass of sand, $m_A=12\text{ kg}$

Mass of iron, $m_B=15\text{ kg}$

Mass of water, $m_C=10\text{ kg}$

Mass of pillow, $m_D=2\text{ kg}$

Formula used:

Weight of an object is given by: $W=mg$

Calculation:

According to the formula, the weight is directly proportional to the mass of the object, because the acceleration due to gravity is constant. So, $W\propto m$

Hence, the ranking is given as follows:

  $m_B>m_A>m_C>m_D$

  $W_B>W_A>W_C>W_D$

Conclusion:

The ranking of materials according to their weight is: $W_B>W_A>W_C>W_D$ .

To determine

Ranking of materials by the normal force the table exerts on them.

Answer to Problem 21A

The ranking of materials by the normal force the table exerts on them is: $N_B>N_A>N_C>N_D$ .

Explanation of Solution

Given:

Mass of sand, $m_A=12\text{ kg}$

Mass of iron, $m_B=15\text{ kg}$

Mass of water, $m_C=10\text{ kg}$

Mass of pillow, $m_D=2\text{ kg}$

Formula used:

The normal force is given by:

  $f=\mu N$

Calculation:

According to the formula, the normal force is directly proportional to the force of friction, because $\mu$ is constant. So, as already done in part (a), we have:

  $f_B>f_A>f_C>f_D$

Hence, the ranking is given as follows:

  $N_B>N_A>N_C>N_D$

Conclusion:

The ranking of materials by the normal force the table exerts on them is: $N_B>N_A>N_C>N_D$ .