Question

На пружину положили 200 граммовый шар. Сила тяжести сжала пружину на 2 м. Вычисли жесткость пружины. Укажи направления силы упругости

Answer 1

Для расчета жесткости пружины воспользуемся формулой:

k = F / x

где k - жесткость пружины, F - сила, действующая на пружину, x - удлинение пружины.

В данном случае, сила, действующая на пружину, равна силе тяжести шара, то есть:

F = m * g

где m - масса шара, g - ускорение свободного падения, принимаем равным 9,8 м/с².

Подставляя известные значения, получим:

F = 0,2 кг * 9,8 м/с² = 1,96 Н

x = 2 м

k = 1,96 Н / 2 м ≈ 0,98 Н/м

Таким образом, жесткость пружины составляет примерно 0,98 Н

Answer 2

Calculation of the Spring Constant

To calculate the spring constant of the given spring, 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. Mathematically, this can be expressed as:

F = k * x

Where: - F is the force exerted by the spring, - k is the spring constant, - x is the displacement of the spring from its equilibrium position.

In this case, we know that the spring is compressed by 2 m and the force exerted by the spring is equal to the weight of the 200-gram ball. To calculate the spring constant, we need to convert the weight of the ball from grams to Newtons.

Conversion of Weight from Grams to Newtons

To convert the weight of the ball from grams to Newtons, we can use the formula:

Weight (in Newtons) = Mass (in kilograms) * Acceleration due to gravity

The mass of the ball is given as 200 grams, which is equal to 0.2 kilograms. The acceleration due to gravity is approximately 9.8 m/s^2.

Therefore, the weight of the ball is:

Weight = 0.2 kg * 9.8 m/s^2

Now, we can calculate the weight of the ball in Newtons.

Calculation of the Spring Constant

Using Hooke's Law and the weight of the ball in Newtons, we can calculate the spring constant.

F = k * x

Substituting the values we have:

Weight = k * x

0.2 kg * 9.8 m/s^2 = k * 2 m

Simplifying the equation:

k = (0.2 kg * 9.8 m/s^2) / 2 m

Now, we can calculate the spring constant.

Calculation:

k = (0.2 kg * 9.8 m/s^2) / 2 m

k = 0.98 N/m

Therefore, the spring constant of the given spring is 0.98 N/m.

Direction of the Restoring Force

The restoring force of a spring always acts in the opposite direction to the displacement of the spring from its equilibrium position. In this case, since the spring is compressed by 2 m, the restoring force will act in the opposite direction, pushing the spring back towards its equilibrium position.

Therefore, the direction of the restoring force is opposite to the direction of the displacement of the spring.