7) For tests using a ballistocardiograph, a patient lies on a horizontal platfor

Question

7) 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 and this recoil can detected to provide information about the heart. For each beat, suppose that 0.05 kg of blood is pushed out of the heart with a velocity of 0.25 m/s and that the mass of the patient and platform is 85 kg. Assuming that the patient does not slip with respect to the platform, and the patient and platform start from rest, determine the recoil velocity.

Explanation / Answer

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 0.050 kg of blood is pushed out of the heart with a velocity of +0.20 m/s and that the mass of the patient and the platform is 90 kg. Assuming that the patient does not slip with respect to the platform, and that the patient and the platform start from rest, determine the recoil velocity. Should be a simple conservation of momentum: 0.050 * 0.2 = 90 * velocity velocity = 0.01/90 m/s

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