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22 April 2018

Why is the net force on a car greater than on the driver?

A reader of my 5 Steps to a 5: AP Physics 1 book sends some kind words about the book, and then asks:

Number 2 in the Forces and Newton's Laws review chapter is about the net force on a driver vs. a drag racer.  To calculate the net force on the drag racer you omit the mass of the driver.  I was wondering about the logistics of that.  How can you only use the mass of the car and not include the driver?  I do understand why the force on the driver only includes the mass of the driver.  The seat exerts the force on the driver's mass.  But that seat force would also be backward on the car, and so to accelerate the car at the acceleration determined would require the additional force on the driver, correct?

The net force on the car is its mass times its acceleration. Sure, the driver may be pushing backward on the car; the road is also pushing forward on the car.  That's all true, but all the question asks for is the net force on the car, which does mean the force of the road minus the force of the driver.  I don't know the value of either of those forces.  I just know about the car's mass and its acceleration.

Similarly, you're right that the only horizontal force on the driver is the force of the car.  That's the net force on the driver.  Yet, that net force is still equal to the driver's mass times her acceleration.

Since the car and driver move together - when one speeds up, the other does too, by the same amount - they have the same acceleration.  Thus ma must be bigger for the more massive car.

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