Question

К свободному концу расположенной на гладком столе пружины жесткостью 50 Н/м прикреплен груз массой 0,2 кг. Пружину растягивают на 0,25 м и затем отпускают. Найдите наибольшую скорость движения груза (массой пружины пренебречь).

Answer 1

Max(v)=max(x)*w=x*корень(к/m)=0,25*корень(50/0,2)  м/с = 3,952847075 м/с ~ 4 м/с

Answer 2

Calculation of Maximum Velocity of the Mass Attached to the Spring

To find the maximum velocity of the mass attached to the spring, we can use the principle of conservation of mechanical energy. The mechanical energy of the system is conserved as the spring oscillates.

The mechanical energy of the system is given by the sum of the potential energy and the kinetic energy:

E = PE + KE

At the maximum displacement of the spring, all the potential energy is converted into kinetic energy. Therefore, at this point, the potential energy is zero and the mechanical energy is equal to the kinetic energy:

E = KE

The potential energy of a spring is given by the formula:

PE = (1/2)kx^2

Where: - PE is the potential energy - k is the spring constant - x is the displacement of the spring from its equilibrium position

The kinetic energy of an object is given by the formula:

KE = (1/2)mv^2

Where: - KE is the kinetic energy - m is the mass of the object - v is the velocity of the object

Setting the potential energy equal to the kinetic energy, we have:

(1/2)kx^2 = (1/2)mv^2

Simplifying the equation, we get:

kx^2 = mv^2

Solving for v, we get:

v = sqrt((kx^2)/m)

Given the following values: - Spring constant (k) = 50 N/m - Mass of the object (m) = 0.2 kg - Displacement of the spring (x) = 0.25 m

Substituting these values into the equation, we can calculate the maximum velocity of the mass attached to the spring:

v = sqrt((50 * 0.25^2) / 0.2)

Calculating this expression, we find that the maximum velocity of the mass attached to the spring is approximately 1.77 m/s.

Please note that the mass of the spring has been neglected in this calculation.