Question

Налетев на пружинный буфер, вагон массой m = 16 т, двигавшийся со скоростью v = 0,6 м/с, остановился, сжав пружину на l = 8 см. Найти общую жесткость k пружин буфера

Answer 1

Calculation of the Total Stiffness of the Spring Buffer

To find the total stiffness (k) of the spring buffer, we can use the formula:

k = F / Δl

Where: - k is the total stiffness of the spring buffer, - F is the force applied to the spring, and - Δl is the compression or deformation of the spring.

In this case, we are given the following information: - Mass of the wagon (m) = 16 tons - Initial velocity of the wagon (v) = 0.6 m/s - Compression of the spring (Δl) = 8 cm

To calculate the force (F), we can use Newton's second law of motion:

F = m * a

Where: - F is the force, - m is the mass, and - a is the acceleration.

Since the wagon comes to a stop, the final velocity (vf) is 0 m/s. Therefore, the acceleration (a) can be calculated using the equation:

vf^2 = vi^2 + 2 * a * Δx

Where: - vf is the final velocity, - vi is the initial velocity, - a is the acceleration, and - Δx is the displacement.

In this case, the final velocity (vf) is 0 m/s, the initial velocity (vi) is 0.6 m/s, and the displacement (Δx) is the compression of the spring (Δl).

Let's calculate the acceleration (a) first:

0^2 = (0.6)^2 + 2 * a * 0.08

Simplifying the equation:

0 = 0.36 + 0.16a

Rearranging the equation:

0.16a = -0.36

a = -0.36 / 0.16

a = -2.25 m/s^2

Now, we can calculate the force (F) using Newton's second law:

F = m * a

F = 16,000 kg * -2.25 m/s^2

F = -36,000 N

Finally, we can calculate the total stiffness (k) of the spring buffer using the formula:

k = F / Δl

k = -36,000 N / 0.08 m

k = -450,000 N/m

Therefore, the total stiffness (k) of the spring buffer is -450,000 N/m.

Please note that the negative sign indicates that the spring is compressed.