Question

An old streetcar rounds a flat corner of radius 6.80 m, at 18.0 km/h. What angle with the vertical will be made by the loosely hanging hand straps?

Answer 1

`\alpha =20.564^(o)`

Step-by-step explanation:

Given data

Radius R=6.80 m

Velocity v=18 km/h =5 m/s

First we need to set up for Force in vertical (y) and horizontal (x)

∑Fy=0=TCosα-W

∑Fx=ma=Fc=TSinα

Solve Vertical force equation for T,substituting mg for W

`TCos\alpha -W=0\\TCos\alpha=W\\TCos\alpha=mg\\T=(mg/Cos\alpha)`

Substitute expression for Fc and T into horizontal force and simplify it we get

`Fc=TSin\alpha\\ where\\Fc=(mv^(2)/R )\\So\\(mv^(2)/R )=(mg/Cos\alpha )Sin\alpha\\(mv^(2)/R )=mg*tan\alpha\\ tan\alpha =(v^(2) )/(Rg)\\ \alpha =tan^(-1)(((5m/s)^(2) )/((6.80m)(9,8m/s^(2) )) )\\ \alpha =20.564^(o)`