An elastic towrope has spring constant 1300 N/m. It's connected between a truck and a 1900-kg car. As the truck tows the car, the rope stretches 55 cm. Starting from rest, how far do the truck and the car move in 1 min? Assume the car experiences negligible friction.

the truck and the car move 586.8 m

Explanation:

Hook's Law: Hook's law state that the force applied to an elastic material is directly proportional to its extension, provided the elastic limit is not exceeded.

From hook's law,

F = ke ... Equation 1

Where F = applied force, k = force constant of the spring or elastic material, e = extension

Given: k = 1300 N/m, e = 55 cm = (55/100) m = 0.55 m.

Substituting these values into Equation 1,

F = 1300 * 0.55

F = 715 N.

But Force (F) = ma ... Equation 2

making a the subject of the equation,

a = F/m ... Equation 3

Where m = mass of the car, a = acceleration of the car.

Given: m = 1900 kg, and F = 715 N

Substituting these values into equation 3

a = 715/1900

a = 0.376 m/s²

Using one of the equation of motion,

S = ut + 1/2at² ... Equation 4

Where S = distance covered, u = initial velocity of the car, t = time, a = acceleration

Given: t = 1 min (1*60) = 60 s, u = 0 m/s (at rest), a = 0.376 m/s²

Substituting these values into equation 4

S = (0 * 60) + 1/2 (0.376*60²)

S = (3600 * 0.376) / 2

S = 586.8 m

Therefore the truck and the car move 586.8 m