Chapter 6, Problem 60AP

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

Chapter
Section

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

# In research in cardiology and exercise physiology, it is often important to know the mast of blood pumped by a person’s bran in one stroke. This information can be obtained by means of a ballistocardiograph. The instrument works as follows: 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 tan be determined independently (e.g., by observing an ultrasound Doppler shift). Assume that the blood’s speed is 50.0 cm/s in one typical trial. The mass of the subject plus the pallet is 54.0 kg. The pallet moves at a speed of 6.00 × 10−5 m in 0.160 s after one heartbeat. Calculate the mass of blood that leaves the heart. Assume that the mass of blood is negligible compared with the total mass of the person. This simplified example illustrates the principle of ballistocardiography, but in practice a more sophisticated model of heart function is used.

To determine
The mass of blood that leaves the heart.

Explanation

Given Info: Distance moved by pallet is Î”c=6.00Ã—10âˆ’5â€‰m and duration of time that pallet moves is Î”t=0.160â€‰s , Mass of the subject plus pallet is M=54.0Â kg , speed of the blood isÂ  and initial momentum of the blood-subject plus pallet system is zero.

The expression for speed is,

V=Î”cÎ”t

• V is the recoil speed of the subject plus pallet.
• Î”c is the distance moved by pallet.
• Î”t is the duration of time that pallet moves after a heartbeat.

Substitute 6.00Ã—10âˆ’5â€‰m for Î”c and 0.160â€‰s for Î”t .

V=6.00Ã—10âˆ’5â€‰m0.160â€‰s=37.5Ã—10âˆ’5â€‰m/s=3.75Ã—10âˆ’4â€‰m/s

Thus the recoil speed of the subject plus pallet is 3.75Ã—10âˆ’4â€‰m/s .

Apply conservation of momentum to blood-subject plus pallet system is,

(mv+MV)f=(mv+MV)i

• m is the mass of the blood that leaves the heart

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