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Understanding Newton's second law is crucial to solving problems involving forces and motion. This fundamental law expresses the relationship between the force acting on an object, its mass, and the acceleration it experiences. The law can be stated as:

• Force = Mass × Acceleration

In mathematical terms: \[ F = ma \] This equation tells us that the force applied to an object is directly proportional to its mass and the acceleration produced. The force is measured in newtons (N), mass in kilograms (kg), and acceleration in meters per second squared (m/s²).In the context of the exercise at hand, we apply this principle to find the net force needed to accelerate the car upward. Once calculated, this net force is added to the gravitational force exerted by the car's weight to ensure the total tension the cable must withstand.

Gravitational force acts on all objects with mass, pulling them towards the center of the Earth. It’s most commonly referred to as "weight" in everyday usage. This force can be calculated using the formula: \[ F_g = mg \] where

• \( F_g \) is the gravitational force,
• \( m \) is the mass of the object (in kg),
• \( g \) is the acceleration due to gravity, approximately \( 9.81 \, \mathrm{m/s^{2}} \) on the surface of the Earth.

In our exercise, the car's mass is known to be \( 1200 \, \mathrm{kg} \). Plugging these values into the formula gives us the gravitational force exerted by the car. This is a key step in finding the total tension in the cable, as this force needs to be counteracted by the tension for the car to move upward.

Acceleration describes the rate at which an object's velocity changes over time. It is a vector quantity, meaning it has both magnitude and direction. The unit of acceleration is meters per second squared (\( \mathrm{m/s^{2}} \)).In cases where an object is accelerating upwards, such as in this exercise, it's essential to calculate the net force required to achieve this acceleration. This involves using Newton's second law, as shown earlier, to determine how much additional force is necessary to overcome not just inertia, but also any opposing forces like gravity.In the given problem, the car needs to be accelerated at \( 0.70 \, \mathrm{m/s^{2}} \). Given the car's mass, we find the required net force needed to achieve this acceleration using the formula:\[ F_{net} = ma \]This gives us a part of the total tension calculation as it reveals how much extra force the cable must exert in addition to balancing the gravitational force.