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)

Answer 1

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#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.