Question

5 к пружине с коэффициентом упругости 200 Н/м подвесили груз № 1, и она растянулась на 4 см. Потом к пружине подвесили груз № 2, и она растяну лась на 6 см. На сколько различаются массы грузов? Ответ: г.

Answer 1

Дано:

k=200 Н/м

x1=4 см=0,04 м

x2=6 см=0,06 м

g≈10 Н/кг

m2-?

m1-?

Решение:

F1=kx1=200×0,04=8 Н

F2=kx2=200×0,06=12 Н

F1=m1g => m1=F1/g=8/10=0,8 кг

F2=m2g =>m2=F2/g=12/10=1,2 кг

m2-m1=1,2-0,8=0,4 кг

Ответ:m1=0,8, m2=1,2; масса груза N2 на 0,4 кг больше чем масса груза N1.

Answer 2

Calculating the Difference in Masses of the Loads on the Spring

To calculate the difference in masses of the loads, we can use the formula for the potential energy stored in a spring:

Potential energy (PE) = 0.5 * k * x^2

Where: - k is the spring constant (given as 200 N/m) - x is the displacement from the equilibrium position

First, we'll calculate the potential energy for each load based on the given displacements.

1. For load #1 (4 cm displacement): - Potential energy = 0.5 * 200 * (0.04)^2 2. For load #2 (6 cm displacement): - Potential energy = 0.5 * 200 * (0.06)^2

The difference in potential energy between the two loads will be directly proportional to the difference in their masses.

Calculating the Difference in Masses

To find the difference in masses, we can use the following relationship:

Difference in potential energy = 0.5 * k * (x2^2 - x1^2)

Where: - x1 is the displacement caused by load #1 - x2 is the displacement caused by load #2

By rearranging the equation, we can solve for the difference in masses:

Difference in mass = (x2^2 - x1^2) / k

Substituting the given values: - x1 = 0.04 m - x2 = 0.06 m - k = 200 N/m

We can now calculate the difference in masses using the provided displacements.

Calculation

Difference in mass = (0.06^2 - 0.04^2) / 200

Difference in mass ≈ 0.0002 kg

Therefore, the difference in masses of the loads is approximately 0.0002 kg.