*The flywheel with the moment of inertia 2 J = 40kg m^2 is under the action of
force moment M =20N.m performs a uniformly variable rotation being in the rest
state from the beginning, Determine the kinetic energy T that the flywheel acquires
through t =10s after the motion start.
*To the spring balance a block is suspended. Through the block, the filament
has been thrown up, the ends of which are loaded with masses m1=1,5kg and
m2 =3,0kg. Define the indications of the balance during the movement. The weight
of the block and filament is neglected.
To determine the kinetic energy acquired by the flywheel after t = 10s, we need to use the equation for rotational kinetic energy:
T = (1/2) * I * ω^2,
where T is the kinetic energy, I is the moment of inertia, and ω is the angular velocity.
We are given the moment of inertia of the flywheel, I = 40 kg m^2, and the force moment acting on it, M = 20 N.m. The torque (τ) generated by the force moment is related to the moment of inertia and angular acceleration (α) by the equation:
τ = I * α.
Since the flywheel is initially at rest, the angular velocity (ω) is zero at the beginning. Using the formula for torque, we can calculate the angular acceleration:
α = τ / I = M / I.
Now, we can find the angular velocity at t = 10s. We use the equation for angular velocity:
ω = α * t,
where t = 10s.
Finally, we substitute the values into the equation for kinetic energy to find T:
T = (1/2) * I * ω^2.
Now let's work on the second question.
To determine the indications of the spring balance during the movement of the block and the filament, we need to consider the forces acting on the system.
When the block is suspended by the filament, it experiences two forces: the tension force in the filament and the weight of the masses. The tension force (T) in the filament is the same throughout its length.
The weight of an object is given by the formula:
Weight = mass * gravity,
where mass is the mass of the object and gravity is the acceleration due to gravity (approximately 9.8 m/s^2).
Considering there are two masses attached to the filament, the total weight acting on the block is the sum of their weights:
Total weight = (mass1 + mass2) * gravity.
The tension force in the filament must balance the total weight of the masses for the block to remain in equilibrium. Therefore, the indications of the spring balance during the movement will show the value of the tension force, which is equal to the total weight of the masses.
Keep in mind that the weight of the block and filament is neglected in this case.