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Students in a technology class are racing cars propelled by carbon dioxide cartridges. A burst of gas is released when the seal of the cartridge is broken, propelling the car down the track. The cartridges are designed to provide a certain impulse. Use the concepts of impulse and momentum to explain why such a cartridge will propel a lighter car to a higher speed.

Answer :

The carbon dioxide cartridge will propel a lighter car to a higher speed because a car with small mass experience a larger change in velocity and a car with large mass experience smaller change in velocity.

In this experiment, gas cartridge provides a certain impulse. Consequently, the mass of gas in cartridge is much less than than the mass of car. We therefore treat it as a constant and write it using this equation below:

Impulse J=Δp=mΔv

Change in velocity (Δv)=Impulse/mass

From the above expressions then clearly a car with small mass experience a larger change in velocity, and a car with large mass experience smaller change in velocity, as we know:

Change in velocity=Impulse/mass

Δv=J/m

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Final answer:

In physics, the concept of impulse changing momentum explains why a lighter CO2 cartridge-powered car will achieve higher speeds. This is due to the lesser mass requiring less force to alter its velocity, a principle directly derived from Newton's Second Law of Motion and conservation of momentum.

Explanation:

Students in a technology class racing cars propelled by carbon dioxide cartridges make use of the physics principle that a lighter car will reach a higher speed due to the foundational concepts of impulse and momentum. Impulse, which is the product of force and time, changes an object's momentum, essentially the quantity of motion the object has. Since momentum (p) is the product of mass (m) and velocity (v), a given impulse will have a larger effect on velocity when the mass is smaller. In simpler terms, as the cartridges provide a certain impulse, a lighter car will gain more speed because it takes less force to change its velocity.

This concept is in accordance with Newton's Second Law of Motion, F = ma or alternatively, the change in momentum (Δp) over time (Δt) equals the net external force (F) applied. When a carbon dioxide cartridge releases gas, it exerts a force on the car over a period, thereby changing the car's momentum. The reason a lighter car accelerates to higher speeds lies in the formula for momentum (p = mv). For the same reason, rockets expel gas to push themselves forward, utilizing the conservation of momentum. While the car's system's total momentum includes both the car and the expelled gases, focusing on the car itself shows that with less mass, more velocity can be achieved with the same amount of force - the thrust provided by the gas.