In research in cardiology and exercise physiology, it is often important to know the mass of blood pumped by a person’s heart 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 υ, and the body and platform move in the opposite direction with speed V The blood velocity can be determined independently (e.g., by observing the Doppler shift of ultrasound). Assume that it is 50.0 cm/s in one typical trial. The mass of the subject plus the pallet is 54.0 kg. The pallet moves 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.)
In research in cardiology and exercise physiology, it is often important to know the mass of blood pumped by a person’s heart 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 υ, and the body and platform move in the opposite direction with speed V The blood velocity can be determined independently (e.g., by observing the Doppler shift of ultrasound). Assume that it is 50.0 cm/s in one typical trial. The mass of the subject plus the pallet is 54.0 kg. The pallet moves 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.)
Solution Summary: The author calculates the mass of blood that leaves the heart by calculating the velocity of the pallet.
In research in cardiology and exercise physiology, it is often important to know the mass of blood pumped by a person’s heart 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 υ, and the body and platform move in the opposite direction with speed V The blood velocity can be determined independently (e.g., by observing the Doppler shift of ultrasound). Assume that it is 50.0 cm/s in one typical trial. The mass of the subject plus the pallet is 54.0 kg. The pallet moves 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.)
In research in cardiology and exercise physiology, it is often important to know the mass of blood pumped by a person’s heart 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 The speed of the blood can 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…
For tests using a ballistocardiograph,
a patient lies on a horizontal
platform that is supported on jets of air Because of the air jets, the
friction impeding the horizontal motion of the platform is
negligible. Each time the heart beats, blood is pushed out of the
heart in a direction that is nearly parallel to the platform. Since
momentum must be conserved, the body and the platform recoil,
and this recoil can be detected to provide information about the
heart. For each beat, suppose that 0.0529 kg of blood is pushed out
of the heart with a velocity of +0.231 m/s and that the mass of the
patient and platform is 80.2 kg. Assuming that the patient does not
slip with respect to the platform, and that the patient and platform
start from rest, determine the recoil velocity.
A time-varying horizontal force F(t) = At3 + Bt2 acts a 10.0-kg object, starting at time t = 1.0 s to t = 5.0 s. In the SI system, A has the numerical value 4.0 and B has the numerical value 3.0.
(a) What are the SI units of A and B?
(b) What impulse does this force impart to the object?
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