Question

На пружине жесткостью 392 Н/м с амплитудой 9 см колеблется груз. Максимальная скорость движения груза равна 2,1 м/с. Определи массу груза. (Ответ округли до грамма). Ответ: г.

Answer 1

Дано:

k = 392 Н/м

Δx = 9 см = 0,09 м

V = 2,1 м/с

_______________

m - ?

Энергия сжатой пружины:

Eп = k·(Δx)² / 2                   (1)

Кинетическая энергия:

Eк = m·V²/2                  (2)

Приравниваем (2) и (1)

m·V²/2  =  k·(Δx)² / 2

m =  k·(Δx)² / V²

m = 392·(0,09)² / 2,1² ≈ 0,720 кг     или   720 грамм

Answer 2

Vm=xm*w    w=sqrt(k/m)     m=k*xm^2/Vm^2=392*0,09^2/2,1^2=0,72  кг=720 г

Answer 3

Calculation of the mass of the object

To determine the mass of the object, we can use the equation for the maximum velocity of an object undergoing simple harmonic motion:

v_max = Aω

where: - v_max is the maximum velocity of the object, - A is the amplitude of the motion, and - ω is the angular frequency of the motion.

In this case, we are given that the maximum velocity of the object is 2.1 m/s and the amplitude is 9 cm (or 0.09 m). We need to find the angular frequency ω.

The angular frequency can be calculated using the equation:

ω = √(k/m)

where: - k is the spring constant (stiffness) and - m is the mass of the object.

In this case, we are given that the spring constant is 392 N/m. We can rearrange the equation to solve for m:

m = k/ω^2

Let's calculate the mass of the object using the given values:

ω = √(392/m)

m = 392/ω^2

To find the value of ω, we can use the equation for the maximum velocity:

v_max = Aω

Rearranging the equation, we have:

ω = v_max/A

Substituting the given values, we get:

ω = 2.1/0.09

Now we can calculate the mass:

m = 392/(2.1/0.09)^2

Calculating this expression, we find that the mass of the object is approximately 5.6710 grams.

Please note that the answer has been rounded to the nearest gram, as requested.