Question

Figure 5-26 shows a train of four blocks being pulled across a frictionless floor by force. What total mass is accelerated to the right by (a) force, (b) cord 3, and (c) cord 1? (d) Rank the blocks according to their accelerations, greatest first. (e) Rank the cords according to their tension, greatest first.

Short answer

1. The total mass accelerated to the right by Force$\stackrel{\rightharpoonup }{\mathrm{F}}$is${\mathrm{M}}_{\mathrm{s}}=20\mathrm{kg}$
2. The total mass accelerated to the right byCord 3 isrole="math" localid="1656999919783" ${\mathrm{M}}_{3\mathrm{c}}=18\mathrm{kg}$
3. The total mass accelerated to the right byCord 1 is${\mathrm{M}}_{1\mathrm{c}}=10\mathrm{kg}$
4. The acceleration of all the blocks is the same.
5. Rank of the cords according to their tension is$\mathrm{cord}3,\mathrm{cord}2,\mathrm{cord}1$

Step-by-step solution

Given information

Masses of the blocks are${\mathrm{m}}_1=2\mathrm{kg},{\mathrm{m}}_2=5\mathrm{kg},{\mathrm{m}}_3=3\mathrm{kg}\mathrm{and}{\mathrm{m}}_4=10\mathrm{kg}$

To understand the concept

The problem is based on Newton’s second law of motion. The law states that the acceleration of an object is dependent on the net force acting upon the object and the mass of the object.

Formula:

${\stackrel{\mathbf{\rightharpoonup }}{\mathbf{F}}}_{net}=\mathbf{m}\overrightarrow{\mathbf{a}}$

(a) To find the total mass accelerated to the right by Force F→

The total mass accelerated to the right by Force $\stackrel{\rightharpoonup }{\mathrm{F}}$is

${\mathrm{M}}_{\mathrm{s}}={\mathrm{m}}_1+{\mathrm{m}}_2+{\mathrm{m}}_3+{\mathrm{m}}_4$

$$\begin{gathered} {\mathrm{M}}_{\mathrm{s}}=2\mathrm{kg}+5\mathrm{kg}+3\mathrm{kg}+10\mathrm{kg} \\ =20\mathrm{kg} \end{gathered}$$

(b) To find the total mass accelerated to the right by Cord 3

The total mass accelerated to the right byCord 3 is

${\mathrm{M}}_{3\mathrm{c}}={\mathrm{m}}_2+{\mathrm{m}}_3+{\mathrm{m}}_4$

$$\begin{gathered} {\mathrm{M}}_{3\mathrm{c}}=5\mathrm{kg}+3\mathrm{kg}+10\mathrm{kg} \\ =18\mathrm{kg} \end{gathered}$$

(c) To find the total mass accelerated to the right by Cord 1

The total mass accelerated to the right byCord 1 is

$$\begin{gathered} {\mathrm{M}}_{1\mathrm{c}}={\mathrm{M}}_4 \\ {\mathrm{M}}_{1\mathrm{c}}=10\mathrm{kg} \end{gathered}$$

(d) To rank the blocks according to their acceleration, the greatest first

As all the masses lie in one system, the acceleration of all the blocks is the same.

Therefore, the rank of the blocks according to their acceleration, greatest first, is a tie.

(e) To rank the cords according to their tension greatest first  

To find the tension, we can multiply the acceleration by the mass on the right-hand side.

Since for cord 3, mass is maximum and acceleration is the same, we can conclude that tension is maximum in cord 3. Similarly, the tension in cord 1 would be minimum.

The rank of the cords according to their tension is$\mathrm{cord}3,\mathrm{cord}2,\mathrm{cord}1$