Question

Помогите!!!! скоростной лифт массой 2000 кг, двигаясь вертикально вверх, производит торможение с ускорением 1 м/с^2. Найти силу натяжения каната лифта и его коэффициент жесткости, если он удлиняется на 0,02 м

Answer 1

Дано    а=-1 м\с2      m=2000 кг    Fн- ?     x- ?

Fн-mg=ma

Fн=mg+ma=2000*(9,8-1)=17600 Н

X=Fн\k=17600\0,02=880 кН\м

Answer 2

Calculation of Tension Force and Spring Constant

To find the tension force in the elevator cable and its spring constant, we can use Newton's second law of motion and Hooke's law.

Given: - Mass of the elevator (m) = 2000 kg - Acceleration (a) = 1 m/s^2 - Elongation of the cable (Δx) = 0.02 m

Step 1: Calculate the tension force (T) in the elevator cable:

The tension force in the cable can be calculated using Newton's second law of motion:

ΣF = ma

In this case, the only force acting on the elevator is the tension force in the cable. Therefore, we can write:

T - mg = ma

where: - T is the tension force in the cable - m is the mass of the elevator - g is the acceleration due to gravity (approximately 9.8 m/s^2)

Rearranging the equation, we get:

T = m(g + a)

Substituting the given values, we have:

T = 2000 kg * (9.8 m/s^2 + 1 m/s^2)

Calculating the tension force:

T = 2000 kg * 10.8 m/s^2 = 21,600 N

Therefore, the tension force in the elevator cable is 21,600 Newtons.

Step 2: Calculate the spring constant (k) of the cable:

The spring constant can be calculated using Hooke's law:

F = kΔx

where: - F is the force applied to the spring - k is the spring constant - Δx is the elongation or compression of the spring

In this case, the force applied to the spring is the tension force in the cable (T), and the elongation of the spring is given as 0.02 m.

Rearranging the equation, we get:

k = F / Δx

Substituting the values, we have:

k = T / Δx

k = 21,600 N / 0.02 m

Calculating the spring constant:

k = 1,080,000 N/m

Therefore, the spring constant of the elevator cable is 1,080,000 N/m.

To summarize: - The tension force in the elevator cable is 21,600 N. - The spring constant of the elevator cable is 1,080,000 N/m.

Please note that the above calculations are based on the given information and assumptions.