Conservation of Momentum problem

AI Thread Summary
A 1500-kg car traveling north at 25 m/s collides with a 2000-kg car moving east at 20 m/s, resulting in both cars sticking together. The initial attempt to solve the problem using scalar momentum equations was incorrect, as the collision involves vector components. After recognizing the need to treat north-south and east-west movements separately, the final velocity was recalculated to be 15.66 m/s. To determine the correct angle for the direction of the final velocity, it is essential to use the tangent function with the east-west component over the north-south component. The angle should be specified as a deviation from north, and checking the relationship between the components can confirm the correct orientation.
Arooj
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Homework Statement


A 1500-kg car is traveling north at 25 m/s when it strikes a 2000-kg car traveling east at 20 m/s. The cars stick together after the collision. What is the final velocity of the two cars?


Homework Equations


m1v1 + m2v2 = (m1 + m2)vf


The Attempt at a Solution


1500(25) + 2000(20) = (1500 + 2000)vf
vf = 22.14 m/s

The answer was incorrect. I then thought vectors would be needed but wasn't sure. Can someone guide me through this problem?
 
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You've used the formula as for scalars, which assumes all movement is in the same dimension. Yes, it's a vector question. Treat NS and EW separately.
 
Thanks, I did so and found the final velocity to be 15.66 m/s. I'm confused on how to find the correct angle to use though for the direction is it the tan x comp over the y comp or the other way around? And how would you know which one it is?
 
Arooj said:
I'm confused on how to find the correct angle to use though for the direction is it the tan x comp over the y comp or the other way around? And how would you know which one it is?
It is standard to give priority to NS, so you should specify the angle as a deviation, E or W, from one of those. That means the tan of the angle will be x over y, in contrast to normal mathematics. You can check whether you have it the right way round by simply seeing which component is the greater and whether the angle is more or less than 45 degrees.
 
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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