Question

Два тягарці різної маси підвішені на одній висоті на нитці, яка перекинута через невагомий блок. Маса одного тягарця в 2 рази більша від маси другого. Через який час від початку руху один тягарець буде на 1 м вище іншого?

Answer 1

Ответ:

см фото

Объяснение:

Answer 2

Problem Analysis

To solve this problem, we can use the principles of mechanics and the concept of work and energy. The scenario described involves two masses of different weights suspended on a thread passing over a weightless pulley. We need to determine the time it takes for one mass to be 1 meter higher than the other.

Solution

Let's denote the masses of the two objects as m1 (the heavier mass) and m2 (the lighter mass). Given that the mass of one object is 2 times greater than the other, we can express this relationship as:

m1 = 2 * m2

The acceleration due to gravity is denoted as g and is approximately 9.81 m/s^2.

Using the Work-Energy Principle

We can use the work-energy principle to solve this problem. The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done by the gravitational force will result in a change in potential energy as the masses move.

The potential energy of an object at a height h above the reference point is given by the formula:

PE = mgh

Where: - PE = potential energy - m = mass of the object - g = acceleration due to gravity - h = height

Calculating the Time Difference

We want to find the time it takes for one mass to be 1 meter higher than the other. Let's denote the time as t.

The difference in potential energy between the two masses when one is 1 meter higher than the other can be expressed as:

ΔPE = m1 * g * (h + 1) - m2 * g * h

Using the relationship m1 = 2 * m2, we can substitute m1 in terms of m2:

ΔPE = 2 * m2 * g * (h + 1) - m2 * g * h

Solving for t: We can use the work-energy principle to find the time difference. The work done by the gravitational force will result in a change in potential energy as the masses move. The difference in potential energy between the two masses when one is 1 meter higher than the other can be expressed as:

ΔPE = m1 * g * (h + 1) - m2 * g * h

Substitute m1 = 2 * m2: ΔPE = 2 * m2 * g * (h + 1) - m2 * g * h

The time t can be calculated using the relationship between work, force, and time:

ΔPE = F * d * cos(θ) Where: - F = force - d = displacement - θ = angle between the force and the displacement

Conclusion

By solving for t using the work-energy principle, we can determine the time it takes for one mass to be 1 meter higher than the other.