A 15-kg steel gas tank holds 300 L of liquid gasoline, having a density of 800 kg / m^3. If the

step 1 So we want to solve for the force needed to decelerate the system at 6 meters per second squared

A 15-kg steel gas tank holds 300 L of liquid gasoline,...

A $15-\mathrm{kg}$ steel gas tank holds $300 \mathrm{L}$ of liquid gasoline, having a density of $800 \mathrm{kg} / \mathrm{m}^{3}$. If the system is decelerated at $6 \mathrm{m} / \mathrm{s}^{2}$ what is the needed force?

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Key Concepts

Newton's Second Law

Newton's Second Law establishes the relationship between force, mass, and acceleration (F = ma). This principle is fundamental in determining the force required to change the velocity of an object, including slowing it down (deceleration).

Mass Calculation from Density

The concept of density provides a means to convert a known volume of a substance into its mass using the relationship mass = density × volume. This is essential when the material’s mass is not given directly but must be determined from its measured volume and known density.

System Mass

In many practical applications, the total mass of a system is the sum of the masses of all its components. Computing this total inertial mass is necessary when calculating the force required to accelerate or decelerate the entire system.

Deceleration

Deceleration, which is simply negative acceleration, implies a reduction in speed. When an object is decelerated, a force must be applied in the direction opposite to its motion. The magnitude of this force can be determined by multiplying the total mass by the rate of deceleration using Newton's Second Law.

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