Finding total weight of a car/ center mass

AI Thread Summary
The total weight of the car is calculated by adding the weights measured at the front and rear wheels, resulting in 4021 lb. The horizontal distance from the rear axle to the center of mass is determined to be approximately 4.98 feet. The discussion highlights the process of solving the problem and confirms the use of the correct formula. Participants express initial confusion but ultimately arrive at the correct answers. The calculations are validated and deemed satisfactory.
wes335
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1. A car has a wheelbase of 9.57 ft. At a weigh station, the driver puts only the front wheels on the scale and measures a weight of 2091 lb. The driver then moves the car and places the rear wheels on the scale and measures a weight of 1930 lb. Find the total weight of the car. Find the horizontal distance from the rear axle to the center mass of the car.



2. Either I'm making this problem way harder than it is, or a I can't find a formula for it.



3. Total weight=2091+1930=4021 lb? Center mass= 4.97766 ft from rear axle.
 
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wes335 said:
1. A car has a wheelbase of 9.57 ft. At a weigh station, the driver puts only the front wheels on the scale and measures a weight of 2091 lb. The driver then moves the car and places the rear wheels on the scale and measures a weight of 1930 lb. Find the total weight of the car. Find the horizontal distance from the rear axle to the center mass of the car.



2. Either I'm making this problem way harder than it is, or a I can't find a formula for it.



3. Total weight=2091+1930=4021 lb? Center mass= 4.97766 ft from rear axle.
That looks good. You should round off the distance from the rear axle to the center of mass to 4.98 feet. Looks like you found the right formula.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

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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