Question

While on a train, you are holding a string with a ball attached to it. At first, the train’s velocity is constant and the string is vertical (the ball hangs straight down). When the train changes direction, while going around a curve with a radius of 300 m, you measure the angle between the string and the vertical to be 35.0 degrees. The ball has a mass of 1.20 kg, and we will use g = 10 N/kg. (a) The speed of the train is constant during this time. What is that speed?
m/s

(b) What is the tension in the string while the train is going around the curve?
N

Answer 1

Answer:

a)  v = 45.37 m/s  and b)  T = 14.4 N

Explanation:

Let's use Newton's second law with centripetal acceleration

     F = ma

Let's set a reference system where the x-axis is horizontal and the y-axis is vertical, in that system the only force to decompose is tension, let's use trigonometry

     sin 35 = Tₓ / T

     cos 35 = $T_{y}$ / T

     Tₓ = T sin35

     $T_{y}$ = T cos 35

Y Axis

    $T_{y}$ -W = 0

    T cos 35 = W

    T = mg / cos 35

X axis

   Tₓ = ma

   a = v² / r

   T sin 35 = m v² / r

   (mg / cos 35) sin 35 = m v² / r

    g tan 35 = v² / r

    v = √ g r tan 35

   

    v = √ (9.8 300 tan 35)

    v = 45.37 m / s

b) the tension of the rope is

    T = mg / cos 35

    T = 1.20 9.8 / cos 35

    T = 14.4 N