finding tension

Question

A 5000 kg tow bus pulls a 2000 kg car horizontally into a garage. If the engine of the tow bus exerts a forward thrust on the bus of 580N, what is the tension in the cable connecting the bus to the car?

Answer 1

Zoey, the first step to handling problems like this is to draw a free body diagram on each object. I like to use varibles to setup the problem and solve for the unknown. Then I plug in the numbers.

 

Let Mb=mass of bus

Let Mc=mass of car

Let T=Tension in cable

 

For the free body diagram of the bus, draw a block, label it Mb, with two horizontal arrows one pointing left and one point right of the box indicating the backward tension and the forward thrust on the bus. Moreover, the bus experiences two forces, the thrust, and the backward tension from the cable.

 

For the free body diagram of the car, draw a box, label it Mc, with the horizontal arrow going to the right indicating the only force the car experiences is the tension from the cable pulling it.

 

∑Fb=580-T=Mb*a Note: a=acceleration and this is using Newton's second law of motion to solve this problem.

∑Fc=T=Mc*a Hence, you got two equations with two unknowns. You could eliminate the variable a solving it from the second equation.

 

a=T/Mc  Substitute this into the first equation to solve for T.

 

580-T=Mb*T/Mc

     +T    +T

580=T+Mb*T/Mc=T(1+Mb/Mc)

 

Hence, T=580/(1+Mb/Mc)=580/(1+5000/2000)=580/(1+2.5)=580/3.5

           T≅166N