Conservation of Motion Collision of two object

AI Thread Summary
The discussion revolves around a physics problem involving the conservation of momentum during a collision between a small car and a larger cart. The small car, with a mass of 0.2 kg, collides with a stationary 3 kg cart, and after the collision, the small car recoils at 0.850 m/s. The user attempts to calculate the final speed of the larger cart using the momentum conservation equation but arrives at an incorrect answer. The key point raised is that this is an elastic collision, meaning the two carts do not move together post-collision, which is crucial for correctly applying the conservation principles. The user seeks clarification on their mistake in the calculations.
kbward
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Homework Statement


A small car is moving at 1.3 m/s on an air track when it collides with a larger 3 kg cart at rest. After the collision, the small cart recoils at 0.850 m/s.
What is the speed of the large cart after the collision?


Homework Equations


m1V1i + m2V2i = (m1+m2)V2f

m1 = .2 kg
m2 = 3 kg
V1i = 1.3 m/s
V2i = 0
V1f = -.85 /ms
V2f = ?

The Attempt at a Solution



.2*1.3 + 3*0= (.2+3) V2f
.26 = 3.2 V2f
V2f = .26/3.2
V2f = .08125

My answer came back wrong. Where am I making a mistake?
Thanks

 
Physics news on Phys.org
If this is an elastic collision, then the carts don't move together after the collision.
 
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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