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

a) v = 45.37 m/s and b) T = 14.4 N

Step-by-step 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