Question

A horizontal rope is attached from a truck to a 1355-kg car. As the truck tows the car on a horizontal straight road, the rope will break if

the tension is greater than 2751 N. Ignoring friction, what is the maximum possible acceleration of the truck if the rope does not break?

Answer 1

Step-by-step explanation:

To find the maximum possible acceleration of the truck without breaking the rope, we need to determine the maximum tension the rope can handle.

We know that the tension in the rope is equal to the force required to accelerate the car. Let's denote the maximum acceleration of the truck as "a" and the mass of the car as "m."

Using Newton's second law of motion, we have:

Tension = Force = mass × acceleration

Given:

Maximum tension (T_max) = 2751 N

Mass of the car (m) = 1355 kg

We can rearrange the equation to solve for the maximum acceleration (a):

a = T_max / m

Substituting the given values:

a = 2751 N / 1355 kg

a ≈ 2.03 m/s²

Therefore, the maximum possible acceleration of the truck, without breaking the rope, is approximately 2.03 m/s².