Question

груз массой 100г на пружине жесткостью 25 Н/м совершает колебания с амплитудой 4см. определите полную механическую энергию маятника и наибольшую скорость движения

Answer 1

E=k*x*x/2

E=25*16/2=200Дж

Answer 2

Calculation of Total Mechanical Energy:

To calculate the total mechanical energy of the spring-mass system, we need to consider both the potential energy and the kinetic energy.

The potential energy of the system is given by the formula:

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

where: - k is the spring constant (also known as the stiffness or the force constant) of the spring, which is given as 25 N/m. - x is the amplitude of the oscillation, which is given as 4 cm (or 0.04 m).

Substituting the given values into the formula, we can calculate the potential energy:

Potential Energy = (1/2) * 25 N/m * (0.04 m)^2

Calculating this expression gives us the potential energy of the system.

Calculation of Maximum Velocity:

The maximum velocity of the mass can be determined using the formula:

Maximum Velocity = sqrt((2 * Total Mechanical Energy) / m)

where: - Total Mechanical Energy is the sum of the potential energy and the kinetic energy of the system. - m is the mass of the object, which is given as 100 g (or 0.1 kg).

Substituting the given values into the formula, we can calculate the maximum velocity:

Maximum Velocity = sqrt((2 * Total Mechanical Energy) / 0.1 kg)

Calculating this expression gives us the maximum velocity of the mass.

Now, let's calculate the total mechanical energy and the maximum velocity using the given values.

Calculation:

Using the given values, we can calculate the total mechanical energy and the maximum velocity of the spring-mass system.

Total Mechanical Energy = Potential Energy + Kinetic Energy

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

Maximum Velocity = sqrt((2 * Total Mechanical Energy) / m)

Substituting the given values: - k = 25 N/m - x = 0.04 m - m = 0.1 kg

into the formulas, we get:

Potential Energy = (1/2) * 25 N/m * (0.04 m)^2

Maximum Velocity = sqrt((2 * Total Mechanical Energy) / 0.1 kg)

Calculating these expressions will give us the values of the total mechanical energy and the maximum velocity.

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