Calculating Final Velocity: 1.5kg Cart with 85g Balls vs 255g Ball at 3.5 m/s"

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The discussion focuses on calculating the final velocity of a 1.5 kg cart after ejecting three 85g balls at 3.5 m/s compared to ejecting a single 255g ball at the same speed. The initial calculations use the principle of conservation of momentum, with participants attempting to solve for the cart's velocity after each scenario. There is confusion regarding the relationship between the cart's speed and the mass of the ejected balls, with one participant asserting that the cart should have a higher final velocity when ejecting multiple lighter balls. The calculations are being revisited to ensure they account for the correct relative speeds and masses. Understanding the momentum conservation principle is crucial for resolving the discrepancies in the results.
dishoom
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Momentum Poblem.. Need help!

A 1.5 kg cart is propelled forward by a series of 85g balls being ejected from the rear of the cart with a speed of 3.5 m/s relative to the cart. Calculate the speed of the cart after three balls have been ejected. Compare this to the speed of the cart if it had ejected a signle 255g ball at 3.5 m/s relative to the cart. Assume negligible friction, calculate the final velocity for each cart?

i have got an answer but the relationship is wrong the first cart should have the faster velocity... anyone help i need to understand this!
 
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dishoom said:
A 1.5 kg cart is propelled forward by a series of 85g balls being ejected from the rear of the cart with a speed of 3.5 m/s relative to the cart. Calculate the speed of the cart after three balls have been ejected.

mv=mv
First Ball:
1.415kg(v)=(0.085kg)(3.5m/s)
solve for v then just do the same for second+third

dishoom said:
Compare this to the speed of the cart if it had ejected a signle 255g ball at 3.5 m/s relative to the cart. Assume negligible friction, calculate the final velocity for each cart?

mv=mv
1.245kg(v)=(0.255kg)(3.5m/s)
solve for v
 
umm... that's not it... it's suppose to be relative to the cart.. i know this cause i did something similar to urs and i got it wrong..
and by the way the mass of balls are seperate...
 
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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