Question

Брусок массой m=200грамм прикреплён к двум упорам с помощью лёгких пружин. Жёсткость первой пружины k1=0,1кн/м, жёсткость второй k2=0,2кн/м. Если в состоянии равновесия бруска первая пружина растянута на x1=12см, то вторая пружина растянута на:?

Answer 1

X²=6см. k²/k1=L1/L²      

Answer 2

Calculating the Extension of the Second Spring

To calculate the extension of the second spring, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to its extension. The formula for Hooke's Law is:

F = kx

Where: - F is the force exerted by the spring, - k is the spring constant (also known as stiffness or rigidity constant), and - x is the displacement from the spring's equilibrium position.

In this case, we have two springs with different spring constants, and we need to find the extension of the second spring when the first spring is stretched to a certain length.

Calculating the Extension of the Second Spring

Given: - Mass of the block, m = 200 grams = 0.2 kg - Stiffness of the first spring, k1 = 0.1 kN/m - Stiffness of the second spring, k2 = 0.2 kN/m - Extension of the first spring, x1 = 12 cm = 0.12 m

We can use the following steps to calculate the extension of the second spring:

1. Calculate the force exerted by the first spring using Hooke's Law: F1 = k1 * x1

2. Calculate the force exerted by the second spring using the equilibrium condition: F2 = m * g, where g is the acceleration due to gravity (approximately 9.81 m/s^2).

3. Use the force exerted by the second spring to find its extension: F2 = k2 * x2

Rearranging the formula to solve for x2: x2 = F2 / k2

Let's perform the calculations.

Calculations

1. Calculate the force exerted by the first spring: F1 = k1 * x1 F1 = 0.1 kN/m * 0.12 m F1 = 0.012 kN

2. Calculate the force exerted by the second spring: F2 = m * g F2 = 0.2 kg * 9.81 m/s^2 F2 = 1.962 N (Newtons)

3. Calculate the extension of the second spring: x2 = F2 / k2 x2 = 1.962 N / 0.2 kN/m x2 = 9.81 m

Answer

The extension of the second spring is 9.81 meters.

Please note that the calculations are based on the given parameters and the assumptions of ideal spring behavior.