Question

Грузовик взял на буксир легковой автомобиль массой 2,4 т и ,двигаясь равноускоренно,за 40 с проехал 200 м. НА сколько удлинялся во время буксировки трос, соединяющий автомобили, если его жесткость 2*10^6 Н/м?

Answer 1

Fупр=kΔx
Fтяги=Fупр=ma
S=at^2/2=200 м 
a=200/800=0.25 м/c^2
Подставим во вторую формулу:
ma=kΔx
2400*0.25=2*10^6*Δx
3=10^4Δx
Δx=0.0003 м= 0.3 мм

Answer 2

Calculation of the Extension of the Towing Cable

To calculate the extension of the towing cable, we can use the formula for the extension of a spring:

Extension = Force / Spring Constant

In this case, the force acting on the towing cable is the tension in the cable, and the spring constant is the stiffness of the cable.

Given: - Mass of the towed car: 2.4 tons (or 2400 kg) - Time taken to travel: 40 seconds - Distance traveled: 200 meters - Stiffness of the cable: 2 * 10^6 N/m

First, let's calculate the force acting on the towing cable using Newton's second law:

Force = Mass * Acceleration

Since the towed car is moving with constant acceleration, we can use the equation of motion:

Distance = Initial Velocity * Time + (1/2) * Acceleration * Time^2

Since the initial velocity is zero, the equation simplifies to:

Distance = (1/2) * Acceleration * Time^2

Rearranging the equation, we can solve for acceleration:

Acceleration = (2 * Distance) / (Time^2)

Now, we can calculate the force:

Force = Mass * Acceleration

Substituting the given values:

Force = 2400 kg * [(2 * 200 m) / (40 s)^2]

Simplifying the equation:

Force = 2400 kg * 0.5 m/s^2

Force = 1200 N

Now, we can calculate the extension of the towing cable:

Extension = Force / Spring Constant

Substituting the given values:

Extension = 1200 N / (2 * 10^6 N/m)

Simplifying the equation:

Extension = 6 * 10^-4 meters

Therefore, the towing cable extended by approximately 0.0006 meters during the towing process.