Newton's second law allows us to find the results for the tension of the rope and the angular acceleration of the body are
a) The angular acceleration is α = 26.7 rad / s²
b) The tension of the rope T = 2.67 N
Given parameters
- The mass of the block m = 1.50 kg
- The radius of the pulley R = 0.30 m
- The moment of inertia I = 0.030 kg m²
To find
Newton's second law indicates that the net force is proportional to the product of the mass and the acceleration of the bodies
∑ F = m a
Where the bold letters indicate vectors, F is the external forces, m the mass and the acceleration of the body
A free body diagram is a diagram of the forces without the details of the bodies, in the attached we see a free body diagram of the system
Let's apply Newton's second law to the block
W - T = m a
Body weight is
W = mg
Let's substitute
mg - T = ma (1)
The pulley is a body that is in rotational motion so we use Newton's second law for rotation
Σ τ = I α
Where τ is the torque, I the moment of inertia and α the angular acceleration
In this case the reference system is located at the turning point
T R = I α
T = [tex]\frac{I \alpha }{R}[/tex]
Linear and angular variables are related
a = α R
We substitute in equation 1 and write the system of equations
mg - T = m α R
T = [tex]\frac{I \alpha }{R}[/tex]
We resolve
mg = α (m R + I / R)
α = [tex]\frac{g}{R + \frac{I}{mR} }[/tex]
We calculate
α = [tex]\frac{ 9.8}{ 0.30+\frac{0.030}{1.50 \ 0.30} }[/tex]
α = 26.7 rad / s²
Let's calculate the tension of the rope
T = [tex]\frac{I \alpha }{R}[/tex]
T = [tex]\frac{0.030 \ 26.7 }{0.30}[/tex]
T = 2.67 N
In conclusion with Newton's second law we can find the results for the tension of the rope and the angular acceleration of the body are
a) The angular acceleration is alpha = 26.7 rad / s²
b) The tension of the rope T = 2.67 N
Learn more here: brainly.com/question/12515285
