An old streetcar rounds a flat corner of radius 9.1 m, at 16 km/h. What angle with the vertical will be made by the loosely hanging hand straps?
The equations I know:
acceleration = velocity squared / radius
(a = v^2 / R)
Force = mass * acceleration
(Fnet = m * a)
Friction = Coefficient * mass * g
(f = U * mass * g)
The Attempt at a Solution
I did some calculations and I am pretty sure I am right so far about these values:
a = 4.444 m / s^2
Not hard to find; just convert 16 km/h to m/s, use the given radius, then plug and chug to find the acceleration.
U = 0.453464
I found this by noting that the centripetal acceleration is due to a single force: the force of static friction pointing towards the center of the turn. Knowing that
f = U * mass * g
And that a = F / mass,
Then a = (U * mass * g) / mass = U * g,
Leaving us with U = a / g = 0.453464.
But now I'm stuck. I have no idea how to generate an angle in this problem. The only angle I see is the 90 degree angle between the force of friction and the normal force or gravity. I thought I might need to construct a triangle with legs l1 = |friction| and l2 = |normal force|, but I have no logic for thinking this and am unsure how to proceed.