Linear momentum and its Conservation

[aaronb]

Homework Statement

The subject lies on a horizontal pallet floating on a film of air. Friction on the pallet is negligible. Initially, the momentum of the system is zero. When the heart beats, it expels a mass m of blood into the aorta with speed v, and the body and platform move in the opposite direction with speed V. The speed of the blood can be determined independently (for example, by observing an ultrasound Doppler shift). Assume that the blood's speed is 54.0 cm/s in one typical trial. The mass of the subject plus the pallet is 54.0 kg. The pallet moves 6.55x10^-5 m in 0.160 s after one heartbeat. Calculate the mass of blood that leaves the heart

Homework Equations

p = mv

The Attempt at a Solution

I set found p=mv initial and final as well. I set initial and final momentum equal to each other and solved for mass of blood. However, my problem is I get a value of 23.4 kg which is intuitively impossible.

 

[Doc Al]

Show how you found that value.

 

[nlightner]

I would approach this problem by first verifying the given information and equations. The equation p=mv is correct for calculating momentum, but it is important to make sure that the units are consistent. In this case, the speed of the blood is given in cm/s, while the mass of the subject and pallet is given in kg. It would be more appropriate to convert the speed to m/s to ensure consistency in units.

Next, I would consider the concept of conservation of momentum. This law states that the total momentum of a closed system remains constant, meaning that the initial momentum must be equal to the final momentum. In this case, the initial momentum is zero, and the final momentum is the combined momentum of the blood and the subject plus pallet. By setting these two equal and solving for the mass of the blood, we should get a more reasonable answer.

Additionally, I would also consider other factors that may affect the movement of the pallet, such as the force of the heartbeat and the angle at which the blood is expelled from the heart. These could potentially affect the results and should be taken into account in the calculations.

In conclusion, as a scientist, I would approach this problem by verifying the given information and equations, considering the concept of conservation of momentum, and taking into account other factors that may affect the results. By doing so, we can ensure that our solution is accurate and reasonable.