Question

Пружину детского пистолета сжимают: в первом случае силой F1= 2 H на 4 см, во втором - неизвестной силой - на 2 см. Отношение потенциальных энергий Еп1/Еп2, приобретённых пружиной в обоих случаях составляет....1) 1/1 2) 1/2 3) 2/1 4) 1/4 5) 4/1 Желательно с решением!!!

Answer 1

K=F1/x1=2/0,04=50 Н\м
F2=k*x2=50*0,02=1 Н
En1=F1*x1/2=2*0,04/2=0,04 Дж
En2=F2*x2/2=1*0,02/2=0,01 Дж
En1/En2=4/1

Answer 2

Problem Analysis

We are given two scenarios involving the compression of a spring in a child's toy gun. In the first scenario, the spring is compressed with a force of F1 = 2 H (H is the unit of force) over a distance of 4 cm. In the second scenario, the spring is compressed with an unknown force over a distance of 2 cm. We need to find the ratio of the potential energies acquired by the spring in both scenarios.

Solution

To solve this problem, we can use the formula for potential energy stored in a spring:

Ep = (1/2) * k * x^2

where Ep is the potential energy, k is the spring constant, and x is the displacement of the spring from its equilibrium position.

In the first scenario, the force applied to the spring is F1 = 2 H and the displacement is x1 = 4 cm = 0.04 m. Let's calculate the potential energy Ep1 acquired by the spring in this scenario.

Ep1 = (1/2) * k * x1^2

In the second scenario, the force applied to the spring is unknown and the displacement is x2 = 2 cm = 0.02 m. Let's calculate the potential energy Ep2 acquired by the spring in this scenario.

Ep2 = (1/2) * k * x2^2

To find the ratio of the potential energies, we can divide Ep1 by Ep2:

Ep1/Ep2 = [(1/2) * k * x1^2] / [(1/2) * k * x2^2]

Simplifying the expression, we can cancel out the common factors:

Ep1/Ep2 = (x1^2) / (x2^2)

Now, let's substitute the given values and calculate the ratio.

Calculation

Given: - F1 = 2 H (force in the first scenario) - x1 = 4 cm = 0.04 m (displacement in the first scenario) - x2 = 2 cm = 0.02 m (displacement in the second scenario)

Using the formula:

Ep1/Ep2 = (x1^2) / (x2^2)

Substituting the values:

Ep1/Ep2 = (0.04^2) / (0.02^2) = 0.0016 / 0.0004 = 4

Therefore, the ratio of the potential energies acquired by the spring in both scenarios is 4.

Answer

The ratio of the potential energies acquired by the spring in the two scenarios is 4.