# Four airline baggage carts are coupled as shown in the figure to make a "train"; each has a mass of 250kg. How do you find the answers to the following questions?

## a. Find the force F that must be applied to accelerate this "train" at $0.8 \frac{m}{s} ^ 2$. b. Find the tension in each of the three couplings between the baggage carts. Jun 25, 2016

$F = 800 N$
${T}_{A B} = 600 N$
${T}_{B C} = 400 N$
${T}_{C D} = 200 N$

#### Explanation:

Given

• $m \to \text{Mass of each bag"=250kg," No . of bag} = 4$
• $a \to \text{acceleration of the train system} = 0.8 \frac{m}{s} ^ 2$

Let Tension on three couplings are

• $\text{Between bag A and B} = {T}_{A B}$

• $\text{Between bag B and C} = {T}_{B C}$

• $\text{Between bag C and D} = {T}_{C D}$

(a) Now the force to be applied on the system for creating
acceleration $a = 0.8 \frac{m}{s} ^ 2$ is given by

$F = 4 \times m \times a = 4 \times 250 \times 0.8 N = 800 N$

(b)

• ${T}_{A B} - 3 \times m \times a = 0$

$\implies {T}_{A B} = 3 \times 250 \times 0.8 = 600 N$

• ${T}_{B C} - 2 \times m \times a = 0$

$\implies {T}_{B C} = 2 \times 250 \times 0.8 = 400 N$

• ${T}_{C D} - 1 \times m \times a = 0$

$\implies {T}_{C D} = 250 \times 0.8 = 200 N$