Question

С какой скоростью двигался вагон массой 20 т перед ударом о стенку, если в момент остановки каждая из двух пружин его буферов оказалось сжатой на 10 см? Известно, что пружина каждого буфера сжимается на 1 см под действием силы 10000Н. Ответ запишите числом в (м/с)

Answer 1

E = kx^2/2 
k = F/x = 10000/0.01 = 1'000'000Н = 1 МН 
Е = 1 МН * 0.01/2 = 5 кДж (энергия пружин) 
Е = mv^2/2 = 5000 (кинетическая энергия = энергия пружин) 
v = корень(2*5000/20000) = корень(2)/2 ~ 0.7 м/с ~ 2.5 км/час

Answer 2

Calculation of the Speed of the Wagon

To calculate the speed of the wagon before it hits the wall, we can use the principle of conservation of mechanical energy. The potential energy stored in the compressed springs of the buffers is converted into kinetic energy as the wagon moves.

The potential energy stored in a spring is given by the formula:

PE = (1/2)kx^2

Where: - PE is the potential energy - k is the spring constant - x is the compression or extension of the spring

In this case, the compression of each spring is 10 cm, or 0.1 m. The force required to compress each spring by 1 cm is 10,000 N.

To find the spring constant, we can rearrange the formula:

k = (2 * PE) / x^2

Substituting the values, we get:

k = (2 * 10,000 N * 0.1 m) / (0.1 m)^2

Simplifying the equation, we find:

k = 200,000 N/m

Now, let's consider the kinetic energy of the wagon just before it hits the wall. The kinetic energy is given by the formula:

KE = (1/2)mv^2

Where: - KE is the kinetic energy - m is the mass of the wagon - v is the velocity of the wagon

The mass of the wagon is given as 20 tons, which is equivalent to 20,000 kg.

We can equate the potential energy stored in the springs to the kinetic energy of the wagon:

(1/2)kx^2 = (1/2)mv^2

Substituting the values, we get:

(1/2)(200,000 N/m)(0.1 m)^2 = (1/2)(20,000 kg)v^2

Simplifying the equation, we find:

v^2 = (200,000 N/m)(0.1 m)^2 / (20,000 kg)

Calculating the right side of the equation, we get:

v^2 = 0.01 m^2/s^2

Taking the square root of both sides, we find:

v = 0.1 m/s

Therefore, the speed of the wagon before it hits the wall is 0.1 m/s.