Ballistocardiography Ballistocardiography is a way to study the functioning of t
ID: 1782358 • Letter: B
Question
Ballistocardiography
Ballistocardiography is a way to study the functioning of the heart that depends on conservation of momentum. The patient lies on a table that is free to move back and forth (along the axis connecting the head and the feet), generally by use of friction reducing rollers. See the figure to the left. As the heart pumps, the blood has velocity and thus momentum. The body then reacts so that momentum is conserved.
A. If the blood’s velocity coming out of the heart, in the middle of the body, is towards the patient’s head, what direction will the patient’s body move to conserve momentum? Let the +X direction be towards the patient’s feet.
B. If each beat causes 85 grams of blood to exit the heart at 35 cm/s, how much momentum, magnitude in kg m/s with direction, does the blood have?
C. If the patient has a mass of 95 kg, what speed, in m/s, will the patient’s body move at in response to each beat of the heart?
D. Circle which of the following scenario(s) would be consistent with the observation that the patient’s body moves SLOWER than the speed measured two months previously. There might be more than one consistent scenario.
The patient has LOST weight (mass) but the heart is functioning the same as before.
The patient has GAINED weight (mass) but the heart is functioning the same as before.
The patient’s weight (mass) is the SAME but the heart pumps LESS blood in each beat with SAME speed as before.
The patient’s weight (mass) is the SAME but the heart pumps MORE blood in each beat with SAME speed as before.
The patient’s weight (mass) is the SAME and the heart pumps the SAME mass of blood in each beat but the blood’s speed is LESS than before.
The patient’s weight (mass) is the SAME and the heart pumps the SAME mass of blood in each beat but the blood’s speed is MORE than before.
Explanation / Answer
(A) if blood moves toward head then body will moves toward feet I.e. along +x axis to balence the momentum
(B) momentum = mV = 85×10-3× 35 ×10-2 kg.m/sec = 2.975 × 10-2 kg.m/sec
(C) let patient moves with velocity v so
Momentum of patient = mv = 95v = 2.975×10-2
it gives v = 3.13 × 10-4 m/sec
(D) Here can be 3 possibility
1. Patient has gained weight but heart is working the same as before .
2. Patient's weight is same but heart pump less blood so momentum will be less.
3. Patient's weight remain same and heart is also pumping at same rate but speed is less compared to before .
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