Question

Допоможіть будь ласка! Паровий молот масою 2 т падає з висоти 2 м, створюючи під час удару силу 14,7 ∙ 10^5 Н. Визначити тривалість удару, якщо удар непружний. Бажано зробити дано і малюнок. (Можете отпримати +бали в моєму профілі питання за цю задачу 100 балів пропонував)

Answer 1

Ответ: 8,6 мс

Объяснение:

Answer 2

To solve this problem, we can use the principle of conservation of momentum and the equation for impulse. The impulse experienced by the steam hammer can be calculated using the equation:

Impulse = Force × Time

Given that the force during the impact is 14.7 × 10^5 N, we can calculate the impulse. Since the impulse is equal to the change in momentum, we can also calculate the change in momentum of the steam hammer.

To find the duration of the impact, we need to determine the change in momentum of the steam hammer. The change in momentum can be calculated using the equation:

Change in momentum = Mass × Velocity

Since the steam hammer falls from a height of 2 m, we can calculate its velocity just before impact using the equation:

Velocity = √(2 × g × height)

where g is the acceleration due to gravity (approximately 9.8 m/s^2).

Let's calculate the values step by step:

Step 1: Calculate the velocity of the steam hammer just before impact

Using the equation for velocity, we can calculate the velocity of the steam hammer just before impact:

Velocity = √(2 × g × height)

Substituting the values, we get:

Velocity = √(2 × 9.8 × 2) m/s

Calculating this, we find:

Velocity ≈ 6.26 m/s

Step 2: Calculate the change in momentum

Using the equation for change in momentum, we can calculate the change in momentum of the steam hammer:

Change in momentum = Mass × Velocity

We know the mass of the steam hammer is 2 t, which is equal to 2000 kg. Substituting the values, we get:

Change in momentum = 2000 kg × 6.26 m/s

Calculating this, we find:

Change in momentum ≈ 12520 kg·m/s

Step 3: Calculate the duration of the impact

Using the equation for impulse, we can calculate the duration of the impact:

Impulse = Force × Time

We know the impulse is equal to the change in momentum, which we calculated to be approximately 12520 kg·m/s. Substituting the values, we get:

12520 kg·m/s = 14.7 × 10^5 N × Time

Solving for Time, we find:

Time ≈ 0.085 s

Therefore, the duration of the impact is approximately 0.085 seconds.

I hope this helps! Let me know if you have any further questions.