Question

при равномерном подъеме платформы с грузом, подъемный кран совершил работу 1000 Дж, а при спуске пустой платформы сила тяжести совершила работу 200 Дж. Во сколько раз масса груза больше массы пустой платформы?

Answer 1

M -масса груза
m -масса платформы
A = (m+M)gh - подъем
A1 = mgh - спуск
A/A1 = (m+M)gh /mgh
1000/200 =(m+M)/m = 1+M/m
5 = 1 +M/m
M/m = 4
ответ в 4 раза

Answer 2

Calculation of the Mass of the Load and the Empty Platform

To determine the ratio of the mass of the load to the mass of the empty platform, we can use the principle of work done. The work done is equal to the force applied multiplied by the distance moved in the direction of the force. In this case, the work done during the upward movement of the platform with the load is 1000 J, and the work done during the downward movement of the empty platform due to gravity is 200 J.

Let's assume the mass of the load is m and the mass of the empty platform is m_empty.

During the upward movement of the platform with the load, the work done is given by the equation:

Work = Force x Distance

Since the platform is moving uniformly, the force applied is equal to the weight of the load, which is m x g, where g is the acceleration due to gravity. The distance moved is not given in the question, so we cannot determine the exact value.

Similarly, during the downward movement of the empty platform, the work done is given by the equation:

Work = Force x Distance

In this case, the force applied is equal to the weight of the empty platform, which is m_empty x g.

From the given information, we have:

Work (upward movement) = 1000 J

Work (downward movement) = 200 J

Using the equations above, we can set up the following equations:

m x g x distance = 1000 J (Equation 1)

m_empty x g x distance = 200 J (Equation 2)

To find the ratio of the mass of the load to the mass of the empty platform, we can divide Equation 1 by Equation 2:

(m x g x distance) / (m_empty x g x distance) = 1000 J / 200 J

Simplifying the equation, we get:

m / m_empty = 1000 J / 200 J

m / m_empty = 5

Therefore, the mass of the load is 5 times the mass of the empty platform.

Please note that the exact values of the mass of the load and the empty platform cannot be determined without additional information. However, we can conclude that the mass of the load is 5 times the mass of the empty platform based on the given work values.