2 sleds tied together are pulled across an icy surface with an applied force of 150 N [E]. The mass of the 1st sled is 18.0 kg and the mass of the last sled is 12.0 kg. The force of friction on each sled is 10 N. Find the magnitude of the tension in the?

rope connecting the two sleds? (Sorry the question was too long)

1 Answer
A08
Jul 12, 2018

Both sleds are pulled together by the applied force as these are tied with a rope. We treat both as one single object. As such these move with the same acceleration.

Total mass of the both sleds #m_T=18.0+12.0=30\ kg#

Tension in the rope does not play any part in the acceleration as it is an internal force.

Using Newton's Second Law of motion we get acceleration as

#veca=vecF_"net"/m_T# .....(1)

Now #vecF_"net"=vecF_"applied"-vecF_"friction"#
#:.vecF_"net"=150-(10+10)=130\ N[E]#

From (1) we get

#veca=130/30=13/3 =4.bar3[E]\ ms^-2# .....(2)

The force with which the second sled is being pulled generates tension #vecT# in the rope. Considering sled 2 or the last sled.

#vecF_"net 2"=vecT-vecF_"friction 2"#
#=>12.0xx4.bar3=T-10#

The magnitude of tension is found by inserting various values

#T=12.0xx4.bar3+10#
#=>T=62\ N#

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