Understanding Weight and Acceleration in a Moving Car

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When a car accelerates, the actual weight of a person inside remains constant, as it is defined by the gravitational force acting on them. However, the apparent weight, which is the normal force exerted by the seat, changes due to the acceleration. This change in apparent weight can be analyzed using free body diagrams to visualize the forces involved. The distinction between actual weight and apparent weight is crucial, as scales measure apparent weight rather than actual weight. Understanding these concepts clarifies how acceleration affects the forces experienced by a person in a moving car.
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I am just looking for some good explanations (or references) to a problem about acceleration. If a person is sitting in a car and the car accelerates then, conceptually, does the weight of the person pushing into the seat increase, decrease, or remain the same?

I extend my thanks to anyone that helps me out.
 
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The weight (look up the definition of weight) will remain constant, however, the normal reaction force exerted by the chair on the person (and hence the person on the chair) will change. You could start by drawing a FBD in order to examine all the forces acting.
 
There are two definitions of weight: "actual weight" and "apparent weight". The "actual weight" of an object is defined as the force on an object due to gravity. The "apparent weight" of an object is the sum of all forces on an object except for gravity. The "actual weight" of a person in a car does not change when the car accelerates. The "apparent weight" does change.

Since force is a vector, so is weight. For an object on the Earth, the "actual weight" vector approximately points toward the center of the Earth while the "apparent weight" points outward. Your bathroom scale (and any device that measures weight, such as an accelerometer) measures "apparent weight", not "actual weight". Actual weight is not measurable. It can only be inferred.
 
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Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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