Question

Жесткость пружины динамометра равна 2Нсм Динамометр постепенно поднимают. Когда показания динамометра стали равны 5 Н, весы показали 1,5 кг. Что будут показывать эти приборы, если динамометр поднять еще на 10 см? Считать, что вес груза с массой 1 кг равен 10 Н, деформацией весов пренебречь.

Answer 1

m₁ = m₂ = m - масса песка равна массе кварца

V₁ = m / ρ₁ - объем песка

V₂ = m / ρ₂ - объем кварца

V₂ * 100 % / V₁ = m *ρ₁ * 100 % / (m * ρ₂) = 1,6 * 100 / 2,6 ≈ 62 %

Answer 2

Calculation of the Spring Constant:

To determine what the instruments will show when the dynamometer is raised by an additional 10 cm, we first need to calculate the spring constant of the dynamometer. The spring constant represents the stiffness of the spring and is denoted by the symbol 'k'.

Given that the stiffness of the spring (k) is equal to 2 N/cm, we can convert it to N/m by multiplying it by 100. Therefore, the spring constant is 200 N/m.

Calculation of the Initial Weight:

When the dynamometer readings reached 5 N, the scales showed a weight of 1.5 kg. To find the weight, we can use the equation:

Weight = Mass x Gravity

Given that the mass of the load is 1 kg and the acceleration due to gravity is approximately 10 N/kg, we can calculate the weight as follows:

Weight = 1 kg x 10 N/kg = 10 N

Therefore, the initial weight shown on the scales is 10 N.

Calculation of the New Weight:

To determine what the instruments will show if the dynamometer is raised by an additional 10 cm, we need to consider the change in potential energy.

When the dynamometer is raised by 10 cm, the change in potential energy can be calculated using the equation:

Change in Potential Energy = Force x Displacement

Given that the force is equal to the weight and the displacement is 10 cm (or 0.1 m), we can calculate the change in potential energy as follows:

Change in Potential Energy = Weight x Displacement = 10 N x 0.1 m = 1 Nm

Since the change in potential energy is equal to the work done on the system, we can equate it to the elastic potential energy stored in the spring:

Change in Potential Energy = (1/2) x k x (Displacement)^2

Substituting the known values, we can solve for the new displacement:

1 Nm = (1/2) x 200 N/m x (Displacement)^2

Simplifying the equation, we find:

Displacement^2 = (1 Nm x 2) / 200 N/m = 0.01 m^2

Taking the square root of both sides, we find:

Displacement = 0.1 m

Therefore, when the dynamometer is raised by an additional 10 cm, the displacement will be 0.1 m.

Calculation of the New Weight Shown on the Scales:

To find the new weight shown on the scales, we can use the equation:

Weight = Mass x Gravity

Given that the mass of the load is 1 kg and the acceleration due to gravity is approximately 10 N/kg, we can calculate the new weight as follows:

Weight = 1 kg x 10 N/kg = 10 N

Therefore, the new weight shown on the scales will still be 10 N.

Conclusion:

When the dynamometer is raised by an additional 10 cm, the instruments will continue to show a weight of 10 N on the scales.