Respuesta :
Answer:
The tension in the rope is 41.38 N.
Explanation:
Given that,
Mass of bucket of water = 14.0 kg
Diameter of cylinder = 0.260 m
Mass of cylinder = 12.1 kg
Distance = 10.7 m
Suppose we need to find that,
What is the tension in the rope while the bucket is falling
We need to calculate the acceleration
Using relation of torque
[tex]\tau=F\times r[/tex]
[tex]I\times\alpha=F\times r[/tex]
Where, I = moment of inertia
[tex]\alpha[/tex] = angular acceleration
[tex]\dfrac{Mr^2}{2}\times\dfrac{a}{r}=F\times r[/tex]
[tex]F=\dfrac{M}{2}a[/tex]...(I)
Here, F = tension
The force is
[tex]F=m(g-a)[/tex]...(II)
Where, F = tension
a = acceleration
From equation (I) and (II)
[tex]\dfrac{M}{2}a=m(g-a)[/tex]
[tex]a=\dfrac{g}{1+\dfrac{M}{2m}}[/tex]
Put the value into the formula
[tex]a=\dfrac{9.8}{1+\dfrac{12.1}{2\times14.0}}[/tex]
[tex]a=6.84\ m/s^2[/tex]
We need to calculate the tension in the rope
Using equation (I)
[tex]F=\dfrac{M}{2}a[/tex]
Put the value into the formula
[tex]F=\dfrac{12.1}{2}\times6.84[/tex]
[tex]F=41.38\ N[/tex]
Hence, The tension in the rope is 41.38 N.
