Question

Через вращающийся вокруг горизонтальной оси блок перекинута невесомая нерастяжимая нить, к концам которой привязаны грузы m1 = 0,5 кг и m2 = 0,6 кг. Найти силу, с которой блок давит на ось при движении грузов. Массой блока и трением в блоке пренебречь

Answer 1

Решение. m2*g-T=m2*a; T-m1*g=m1*a; a=(g*(m2-m1))/(m2+m1); T=m1*g*(1+(m2-m1))/(m2+m1))=(2*m1*m2*g)/(m1+m2); F=2*T;    Ну как то так.....

Answer 2

Calculation of the Force Exerted by the Block on the Axis

To find the force with which the block presses on the axis during the movement of the loads, we can use the principle of conservation of angular momentum. Since the block is rotating around a horizontal axis, the angular momentum of the system remains constant.

The angular momentum of the system can be calculated as the product of the moment of inertia and the angular velocity. In this case, the moment of inertia is given by the sum of the moments of inertia of the two masses, m1 and m2, about the axis of rotation.

The moment of inertia of a point mass rotating about an axis is given by the formula I = m * r^2, where m is the mass of the point mass and r is the distance of the point mass from the axis of rotation.

Let's assume that the distance of the masses from the axis of rotation is r. Therefore, the moment of inertia of m1 is I1 = m1 * r^2 and the moment of inertia of m2 is I2 = m2 * r^2.

Since the block is rotating around a horizontal axis, the angular velocity of the system is the same for both masses.

According to the conservation of angular momentum, the initial angular momentum of the system is equal to the final angular momentum of the system. The initial angular momentum is given by the sum of the angular momenta of m1 and m2, and the final angular momentum is given by the product of the moment of inertia of the system and the final angular velocity.

Therefore, we can write the equation:

I1 * ω + I2 * ω = (I1 + I2) * ω

Simplifying the equation, we get:

m1 * r^2 * ω + m2 * r^2 * ω = (m1 * r^2 + m2 * r^2) * ω

Canceling out the common factors, we have:

m1 * ω + m2 * ω = (m1 + m2) * ω

Since the angular velocity ω is the same for both masses, we can factor it out:

( m1 + m2 ) * ω = F * r

Where F is the force with which the block presses on the axis, and r is the distance of the masses from the axis of rotation.

Therefore, the force exerted by the block on the axis can be calculated as:

F = ( m1 + m2 ) * ω / r .

Now, let's substitute the given values into the equation to find the force.

Given: m1 = 0.5 kg m2 = 0.6 kg

We need to find the force F.

Since the problem does not provide the value of the angular velocity ω or the distance r, we cannot calculate the force without this information. Please provide the values of ω and r to proceed with the calculation.