Question

Explain in terms of momentum and Newton’s laws how a car’s air resistance is due in part to the fact that it pushes air in its direction of motion.

Short answer

According to Newton’s second law

Net force =\({F_{net}} = mass \times acceleration\)

Newton’s second law states that, in an inertial frame of refrence,the vector sum of all the forces acting on an object equals the mass of that object multiplied by its acceleration.

According to Newton’s third law if car pushes the air, the air also pushes the car because action-reaction forces act on different objects.

Step-by-step solution

Relation between force and change in momentm

The rate of change of momentum with respect to time is defined as force. The second law of Newton

\(\begin{aligned}{F_{net}} &= mass \times acceleration\\{F_{net}} &= m\dfrac{{\Delta v}}{{\Delta t}}\\{F_{net}} &= \dfrac{{\Delta P}}{{\Delta t}}\\\overrightarrow {{F_{net}}} &= \dfrac{{\overrightarrow {\Delta P} }}{{\Delta t}}\end{aligned}\)

The force acts in the direction of change in momentum.

Step 2: Explaining in terms of momentum and Newton’s laws how a car’s air resistance is due in part to the fact that it pushes air in its direction of motion

When car moves it pushes the air in forward direction. The push is a kind of a force. When the air is pushed forward by the action of the car , the reaction force will be on car in backward direction.

According to Newton’s third law if there is an action then there will be an equal and opposite reaction but the action-reaction forces act on different bodies.

Therefore, when car pushes the air forward then the air pushes the car in backward direction with the same force.

Reaction force is acting on the car opposite to the direction of motion of the car , therefore it will decrease the velocity of the car. So,final velocity of the car is less than the initial velocity.

\(\begin{aligned}\overrightarrow {{F_{net}}} &= \dfrac{{\overrightarrow {\Delta P} }}{{\Delta t}}\\\overrightarrow {{F_{net}}} &= \dfrac{{m(\overrightarrow {{v_f}} - \overrightarrow {{v_i}} )}}{{\Delta t}}\\{v_f} &< {v_i}\\so,\overrightarrow {{F_{net}}} &= - ve\end{aligned}\)

The negative sign indicates that the direction of the force is opposite to the motion of the motion. So, it resist the motion of the car or it’s a resistance force.Hencea car’s air resistance is due in part to the fact that it pushes air in its direction of motion.