Chapter 4, Problem 19P

A box weighing 77.0 N rests on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-45). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs (a) 30.0 N, (b) 60.0 N, and (c) 90.0 N.

To determine

The force exerted on the box by the table when 30 N weight is hanging on the other side.

Answer to Problem 19P

Solution:

For exerted on the box by the table is $47N$ .

Explanation of Solution

Given:

Weight of the box at the table, $W_T=77\text{ N}$

Weight of the box hanging on the other side, $W_h=30\text{ N}$

System is at rest as hanging weight is less than weight on the table, $a=0{\text{ m/s}}^{\text{2}}$

To find:

(I) Tension along the rope, $T=?$

(II) Force exerted on box by the table, $F_T=?$

Formula:

From Newton’s second law of motion:

  ${\displaystyle \sum F}=ma$

Where, m is mass and a is acceleration.

Calculations:

(I) Fortension in the rope.

  

  $\begin{array}{l}{\displaystyle \sum F}=ma\\ W_H-T=ma\\ 30-T=m\left(0\right)\\ T=30\text{N}\end{array}$

(II) For force that table exerts on the block.

  

  $\begin{array}{l}{\displaystyle \sum F}=ma\\ F_T-W_T+T=ma\\ F_T+ 30– 77=m\left(0\right)\\ F_T=47N\end{array}$

Conclusion: Using Newton’s law, the force on the box bythe table is equal to $47N$ .

To determine

The force exerted on the box by the table when 60 N weight is hanging on other side.

Answer to Problem 19P

Solution:

Force exerted by the table on the box is 17 N.

Explanation of Solution

Given:

Weight of the box at the table, $W_T=77\text{ N}$

Weight of the box hanging on the other side, $W_h=60\text{ N}$

System is at rest as hanging weight is less than weight on the table, $a=0{\text{ m/s}}^{\text{2}}$

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To find:

(I) Tension along the rope, $T=?$

(II) Force exerted on the box by the table, $F_T=?$

Formula:

From Newton’s second law of motion:

  ${\displaystyle \sum F}=ma$

Where, m is the mass and a is the acceleration.

Calculations:

(I) For hanging weight.

  

  $\begin{array}{l}{\displaystyle \sum F}=ma\\ W_h-T=ma\\ 60-T=m\left(0\right) \\ T=60\text{ N}\end{array}$

(II) For a mass on the table.

  

  $\begin{array}{l}{\displaystyle \sum F}=ma\\ F_T+T-W_T=ma\\ F_T+ 60–77 =m\left(0\right)\\ F_T=17N\end{array}$

Conclusion: Newton’s second law of motion helps to calculate the force exerted by the table on the box equal to $17N$ .

To determine

The force exerted on the box by the table when 90 N weightis hanging on another side.

Answer to Problem 19P

Solution:

Force exerted on the box equal to 0 N.

Explanation of Solution

Given:

Weight of the box at the table, $W_T=77\text{ N}$

Weight of the box hanging on the other side, $W_h=90\text{ N}$

System is at rest as hanging weight is less than weight on the table, $a=0{\text{ m/s}}^{\text{2}}$

To find:

(I) Tension along the rope, $T=?$

(II) Force exerted on box by the table, $F_T=?$

• Hanging weight is more than weight on the table.
• This arrangement makes the hanging box move downward and box on the table move upward.
• Box moving upward no longerremains in contact with the table.
• The normal force $F_T$ is contact force.
Hence, in absence of contact, contact force $F_T$ ceases to zero instantly.

Conclusion: In absence of contact, table exerts no force on the box.