Answer:
v = 4.25 m / s
Explanation:
To solve this exercise we must use Newton's second law, let's set a reference system that is horizontal and vertical
Axis y
- W = 0
X axis
Tₓ = m a
The acceleration is centripetal
a = v² / r
Tₓ = m v² / r
v² = Tₓ r / m (1)
Let's use trigonometry to find the tension components,
sin θ = Tₓ / T
cos θ = / T
= T cos θ
Tₓ = T sin θ
Let's look angle for the maximum tension 103 N
= T cos θ = W
θ = cos⁻¹ W / T
θ = cos⁻¹ (5.77 9.8 / 103)
θ = 56.7°
Now let's find the radius of the circle
sin 56.7 = r / L
r = L sin 56.7
We substitute in the speed equation (1)
v² = T sin 56.7 L sin 56.7 / m
v = √ T L sin² 56.7 / m
Let's calculate
v = √ (103 1.45 sin² 56.7 /5.77)
v = 4. 25 m / s