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.

1 Answer
Jun 25, 2016

Answer:

#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#