Question

Падающим с высоты 1,2 м грузом забивают сваю, которая от удара уходит в землю на 2 см. Определите силу удара и его продолжительность, если масса груза 500 кг, а масса сваи намного меньше массы груза. Помогите!!! Срочно надо!

Answer 1

Потенциальная энергия сваи m*g*h идет в итоге на совершение работы F*s
По закону сохранения энергии m*g*h=F*s
F=m*g*h/s=500*10*1,2/0,02=300000 Н=300 кН

Answer 2

Calculation of Impact Force and Duration

To determine the impact force and duration when a load of 500 kg falls from a height of 1.2 m and drives a pile into the ground by 2 cm, we can use the principle of conservation of energy. The potential energy of the falling load is converted into kinetic energy, which is then transferred to the pile upon impact.

The potential energy of the load can be calculated using the formula:

Potential Energy = mass × gravity × height

Given that the mass of the load is 500 kg and the height is 1.2 m, we can calculate the potential energy:

Potential Energy = 500 kg × 9.8 m/s^2 × 1.2 m

To calculate the impact force, we need to know the duration of the impact. Unfortunately, the duration of the impact is not provided in the question. However, we can make an assumption that the duration of the impact is very short, approaching zero. This assumption allows us to calculate the impact force using the formula:

Impact Force = Change in Momentum / Duration of Impact

Since the duration of the impact is assumed to be very short, the change in momentum can be approximated as the product of the mass of the load and the velocity at impact. The velocity at impact can be calculated using the principle of conservation of energy:

Potential Energy = Kinetic Energy

Potential Energy = (1/2) × mass × velocity^2

By rearranging the equation and solving for velocity, we can find the velocity at impact:

velocity = sqrt((2 × Potential Energy) / mass)

Now we can calculate the impact force:

Impact Force = mass × velocity / Duration of Impact

However, since the duration of the impact is assumed to be very short, we can simplify the equation further:

Impact Force ≈ mass × velocity

To find the duration of the impact, we need to know the distance the pile is driven into the ground. Given that the pile is driven into the ground by 2 cm, we can calculate the duration of the impact using the formula:

Duration of Impact = Distance / Velocity

Substituting the values, we can calculate the duration of the impact.

Calculation Steps:

1. Calculate the potential energy of the falling load: - Potential Energy = 500 kg × 9.8 m/s^2 × 1.2 m

2. Calculate the velocity at impact: - velocity = sqrt((2 × Potential Energy) / mass)

3. Calculate the impact force: - Impact Force ≈ mass × velocity

4. Calculate the duration of the impact: - Duration of Impact = Distance / Velocity

Let's perform the calculations:

1. Calculate the potential energy: - Potential Energy = 500 kg × 9.8 m/s^2 × 1.2 m - Potential Energy = 5880 J

2. Calculate the velocity at impact: - velocity = sqrt((2 × Potential Energy) / mass) - velocity = sqrt((2 × 5880 J) / 500 kg) - velocity ≈ 10.88 m/s

3. Calculate the impact force: - Impact Force ≈ mass × velocity - Impact Force ≈ 500 kg × 10.88 m/s - Impact Force ≈ 5440 N

4. Calculate the duration of the impact: - Duration of Impact = Distance / Velocity - Duration of Impact = 0.02 m / 10.88 m/s - Duration of Impact ≈ 0.0018 s

Therefore, the approximate impact force is 5440 N, and the approximate duration of the impact is 0.0018 seconds.

Please note that these calculations are based on the assumptions made and the given information.