Generic KE problem with a twist.

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AI Thread Summary
The discussion revolves around a physics problem involving two cars with different velocities and the calculation of stopping distance. The initial analysis suggested that without knowing the masses of the cars, it was impossible to determine the correct answer. However, the teacher marked option B (1/4 the distance) as correct, raising questions about how braking distance can be calculated without specific mass or braking capability data. The conversation highlights the complexities of kinetic energy and braking forces, suggesting that mass may influence the friction force in a way that allows for a generalized solution. Ultimately, the problem illustrates the nuances of physics calculations in real-world scenarios.
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Homework Statement


"Two cars are traveling along a road, and one is going at half the velocity of the other one. What is the distance required to come to a stop for the car going at the slower speed relative to the faster car."

The possible answers listed were as:
A:1/2 the distance
B:1/4 the distance
C:Not enough info provided


Homework Equations


I suppose it would be KE=1/2m·v^2


The Attempt at a Solution


At first glance I plugged in a mass of 2000kg for each and a speed of 20m/s for the fast one and 10m/s for the slow one. The resulting KE's came out to be 40,000 and 10,000 respectively. However after reading the problem I discovered that it was not stated that the masses were equal, so I answered not enough info. Upon receiving my test back, lo and behold my teacher marked that B was in fact correct. My question is, how is it possible to calculate the braking distance without knowing the masses of the cars, and without also knowing the braking capability of each car. i.e. A Ferrari Enzo can brake from 60-0 in 109 ft, whereas a 2005 Volkswagen Jetta takes 130 ft. to stop 60-0 (both cars weighing 3230 lbs).
 
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Great question. Your initial intuitive answer is the same as mine, but maybe increasing mass increases the F=mu*N friction force enough to offest it in the ideal?
 
Last edited:
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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