Question

Пружина жёсткостью 160 Н/м выталкивает груз массой 100 г вертикально вверх. На сколько была сжата пружина, если груз был подброшен на высоту 5 м? чему равно сжатие пружины м?

Answer 1

Ответ:

Объяснение:

Дано:

k = 160 Н/м

m = 100 г = 0,1 кг

h = 5 м

____________

Δx - ?

1)

Потенциальная энергия груза на высоте h:

Eп = m·g·h = 0,1·10·5 = 5 Дж                      (1)

2)

Потенциальна энергия сжатой пружины:

Eп₁ = k·Δx² / 2 = 160·Δx² / 2 = 80·Δx²        (2)

3)

Поскольку эти энергии равны по закону сохранения энергии, то приравняем (2) и (1):

80·Δx² = 5

Δx = √ (5/80) ≈ 0,25 м

Answer 2

Calculation of the Compression of the Spring

To calculate the compression of the spring, we can use the principle of conservation of mechanical energy. The potential energy gained by the mass when it is lifted to a certain height is equal to the potential energy stored in the compressed spring.

The potential energy gained by the mass can be calculated using the formula:

Potential Energy = mass * gravity * height

Given: - Mass of the object (m) = 100 g = 0.1 kg - Height (h) = 5 m - Gravity (g) = 9.8 m/s^2 (approximate value on Earth)

Using the formula, we can calculate the potential energy gained by the mass:

Potential Energy = 0.1 kg * 9.8 m/s^2 * 5 m

Now, we need to equate this potential energy to the potential energy stored in the compressed spring. The potential energy stored in a spring can be calculated using Hooke's Law:

Potential Energy = (1/2) * k * x^2

Where: - k is the spring constant (stiffness) in N/m - x is the compression of the spring in meters

We are given the spring constant (stiffness) of the spring, which is 160 N/m.

Equating the potential energy gained by the mass to the potential energy stored in the compressed spring, we can solve for the compression of the spring (x):

(1/2) * k * x^2 = mass * gravity * height

Substituting the given values:

(1/2) * 160 N/m * x^2 = 0.1 kg * 9.8 m/s^2 * 5 m

Simplifying the equation:

80 N/m * x^2 = 0.49 kg * m^2/s^2

Dividing both sides of the equation by 80 N/m:

x^2 = 0.49 kg * m^2/s^2 / 80 N/m

Taking the square root of both sides of the equation:

x = sqrt(0.49 kg * m^2/s^2 / 80 N/m)

Evaluating the expression:

x ≈ 0.088 m

Therefore, the compression of the spring is approximately 0.088 meters (or 8.8 cm).

Please note that the above calculation assumes ideal conditions and neglects factors such as air resistance and energy losses due to friction.