Question

Коли за допомогою рухомого блока рівномірно піднімають вантаж масою 30кг, вільний кінець шнура тягнуть із силою 200Н. Визначте К.К.Д. рухомого блока.

Answer 1

1. Знайдемо силу з якою б можна було підняти,знаючи,що рухомий блок дає виграш у силі в два рази:

а) Знайдемо спочатку вагу тіла:

 $P=m\cdot{g}=30\cdot{9,8}=300 H$приблизно

б) А тепер і силу:

 $F=\frac{P}{2}=\frac{300}{2}=150 H$

2. Так як ККД - це  відношення корисної роботи до повної,а висота,на яку підіймають вантаж у будь-якому вмпадку однакова,то приймемо її за 1,то відношення сил і буде ККД:

ККД=150/200=0,75 или 75% 

Answer 2

Calculation of Mechanical Efficiency of a Moving Block

To calculate the mechanical efficiency of a moving block, we need to determine the work input and work output of the system. The mechanical efficiency (η) is defined as the ratio of the useful work output to the work input.

Work Input

The work input (W_in) is the product of the force applied and the distance over which the force is applied. In this case, the force applied is the tension in the rope (T) and the distance is the height (h) through which the load is lifted.

Work Output

The work output (W_out) is the product of the weight of the load (mg) and the height (h) through which it is lifted.

Calculation

To calculate the mechanical efficiency, we can use the following formula:

η = W_out / W_in

Let's calculate the work input and work output:

- Mass of the load (m): 30 kg - Force applied (T): 200 N - Height through which the load is lifted (h): unknown

To find the height (h), we need to know the acceleration due to gravity (g). Assuming a standard value of 9.8 m/s² for g, we can calculate the height using the formula:

W_out = mgh

Now, let's calculate the work input and work output:

Work Input (W_in): - Force applied (T): 200 N - Distance (h): unknown

Work Output (W_out): - Mass of the load (m): 30 kg - Height (h): unknown - Acceleration due to gravity (g): 9.8 m/s²

To find the mechanical efficiency (η), we need to calculate the work input and work output and then divide the work output by the work input.

Calculation Steps:

1. Calculate the work output (W_out): - W_out = mgh - W_out = 30 kg * g * h

2. Calculate the work input (W_in): - W_in = T * d - W_in = 200 N * d

3. Calculate the mechanical efficiency (η): - η = W_out / W_in

Let's calculate the mechanical efficiency using the given values.