Question

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 `0.8m/s^2`.
b. Find the tension in each of the three couplings between the baggage carts.

Answer 1

`F =800N`
`T_(AB)=600N`
`T_(BC)=400N`
`T_(CD)=200N`

Explanation:

Given

• `m-> "Mass of each bag"=250kg," No . of bag"=4`
• `a-> "acceleration of the train system"=0.8m/s^2`

Let Tension on three couplings are

• `"Between bag A and B"=T_(AB)`

• `"Between bag B and C"=T_(BC)`

• `"Between bag C and D"=T_(CD)`

(a) Now the force to be applied on the system for creating
acceleration `a=0.8m/s^2` is given by

`F = 4xxmxxa=4xx250xx0.8N=800N`

(b)

• `T_(AB)-3xxmxxa=0`

`=>T_(AB)=3xx250xx0.8=600N`

• `T_(BC)-2xxmxxa=0`

`=>T_(BC)=2xx250xx0.8=400N`

• `T_(CD)-1xxmxxa=0`

`=>T_(CD)=250xx0.8=200N`