Question

К динамометру привязан груз массой 2 кг. Динамометр с грузом опускают с ускорением 3 м/с2. Жёсткость пружины 103 Н/м. Определите модуль растяжения пружины динамометра

Answer 1

F=m*(g-a)
x=F/k=m*(g-a)/k=2*(10-3)/1000=0,014 м=1,4 см

Answer 2

Calculation of the Spring Constant

To determine the modulus of elasticity of the spring in the dynamometer, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.

Hooke's Law can be expressed as:

F = k * x

Where: - F is the force applied to the spring, - k is the spring constant (also known as the modulus of elasticity), and - x is the displacement of the spring from its equilibrium position.

In this case, the force applied to the spring is equal to the weight of the mass attached to the dynamometer, which is given as 2 kg. The acceleration with which the dynamometer and the mass are lowered is 3 m/s^2.

To calculate the spring constant, we need to determine the displacement of the spring. Since the dynamometer and the mass are being lowered, the displacement is equal to the distance traveled by the dynamometer and the mass.

Let's calculate the displacement:

s = (1/2) * a * t^2

Where: - s is the displacement, - a is the acceleration, and - t is the time.

Since the dynamometer and the mass are being lowered, the acceleration is negative (-3 m/s^2). The time is not provided in the question, so we cannot calculate the exact displacement without that information.

However, we can proceed with the calculation using a hypothetical time value for illustrative purposes. Let's assume the time is 1 second.

Using the given values: - a = -3 m/s^2 (negative because the dynamometer and the mass are being lowered), - t = 1 s,

We can calculate the displacement:

s = (1/2) * (-3 m/s^2) * (1 s)^2 = -1.5 m

Now, let's calculate the spring constant using Hooke's Law:

F = k * x

mg = k * x

Where: - m is the mass (2 kg), - g is the acceleration due to gravity (approximately 9.8 m/s^2), and - x is the displacement (-1.5 m).

Substituting the values:

2 kg * 9.8 m/s^2 = k * (-1.5 m)

Simplifying:

k = (2 kg * 9.8 m/s^2) / (-1.5 m)

k ≈ -12.93 N/m

Therefore, the modulus of elasticity (spring constant) of the spring in the dynamometer is approximately 12.93 N/m.