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For tests using a ballistocardiograph, a patient lies on ahorizontal platform that is supported on jets of air. Because ofthe air jets, the friction impeding the horizontal motion of theplatform is negligible. Each time the heart beats, blood is pushedout of the heart in a direction that is nearly parallel to theplatform. Since momentum must be conserved, the body and theplatform recoil, and this recoil can be detected to provideinformation about the heart. For each beat, suppose that 0.050 kgof blood is pushed out of the heart with a velocity of +0.30 m/s and thatthe mass of the patient and the platform is 85 kg. Assuming that the patient does not slipwith respect to the platform, and that the patient and the platformstart from rest, determine the recoil velocity.
_________ m/s

Sagot :

Answer:

   v ’= - 1.76 10⁻⁴ m / s

Explanation:

We can solve this problem using momentum conservation. Defined a system formed by the patient, his blood and the platform in such a way that the forces are internal and the moment is conserved

initial instnate. Before pumping

        p₀ = 0

final instant. Right after the heart pumping

        p_f = m v + M v'

where m is the mass of blood and M the mass of the patient + the platform

       p₀ = p_f

       0 = m v + M v’

       v ’=  - [tex]\frac{m}{M} \ v[/tex]

let's calculate

       v ’= - [tex]\frac{0.050}{85}[/tex]  0.30

       v ’= - 1.76 10⁻⁴ m / s

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