Respuesta :
Answer:
F = 0.535 N
Explanation:
Let's use the concepts of energy, at the highest and lowest point of the trajectory
Higher
Em₀ = U = mg y
Lower
[tex]Em_{f}[/tex] = K = ½ m v²
Emo =[tex]Em_{f}[/tex]
mg y = ½ m v2
v = √ 2gy
y = L - L cos θ
v = √ (2g L (1-cos θ))
Now let's use Newton's second law n at the lowest point where the acceleration is centripetal
F = ma
a = v² / r
In turning radius is the cable length r = L
F = m 2g (1-cos θ)
Let's calculate
F = 2 1.25 9.8 (1 - cos 12)
F = 0.535 N
The tension in the rope when the ball is at the lowest point is 0.535 newtons.
What is energy conversion?
The sum of kinetic energy and the potential energy of the body is constant. which is the energy of the remains conserved. This is known as energy conversion.
A (1.25) kg bowling ball is hung on a (2.50) m long rope. It is then pulled back until the rope makes an angle of (12.0)° with the vertical and released.
The initial energy of the body and the final energy of the body will be equal.
[tex]\rm E_i = E_f\\\\mgx = \dfrac{1}{2} m v^2\\\\v = \sqrt{2gx}[/tex]
We have,
[tex]x = l-lcos \theta[/tex]
Then
[tex]\rm E_i = E_f\\\\mgx = \dfrac{1}{2} m v^2\\\\v = \sqrt{2g(l-l*cos \theta)}[/tex]
From newton's second law, we have
[tex]\rm F = ma\\\\and \\\\a = \dfrac{v^2}{r}\\[/tex]
In turn, a radius of a cable will be r = l
[tex]\rm F = m *2g(1-cos \theta)\\\\F = 2*1.25*9.81(1-cos \ 12^o)\\\\F = 0.535 \ N[/tex]
The tension in the rope when the ball is at the lowest point is 0.535 newtons.
More about the energy conservation link is given below.
https://brainly.com/question/2137260
