In a research facility, a person lies on a horizontal platform which floats on a film of air. When the person's heart beats, it pushes a mass m of blood into the aorta with speed v, and the body and platform move in the opposite direction with speed V. Assume that the blood's speed is 56.5 cm/s. The mass of the person + platform is 54.0 kg. The platform moves 6.30 ✕ 10-5 m in 0.160 s after one heartbeat. Calculate the mass (in g) of blood that leaves the heart. Assume that the mass of blood is negligible compared with the total mass of the person, and the person + platform is initially at rest. (Also assume that the changes in velocity are instantaneous.)

Question

Physics

Werner

2 March, 05:36

In a research facility, a person lies on a horizontal platform which floats on a film of air. When the person's heart beats, it pushes a mass m of blood into the aorta with speed v, and the body and platform move in the opposite direction with speed V. Assume that the blood's speed is 56.5 cm/s. The mass of the person + platform is 54.0 kg. The platform moves 6.30 ✕ 10-5 m in 0.160 s after one heartbeat. Calculate the mass (in g) of blood that leaves the heart. Assume that the mass of blood is negligible compared with the total mass of the person, and the person + platform is initially at rest. (Also assume that the changes in velocity are instantaneous.)

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Answers (2)

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Jordyn Irwin · Answer 1

Answer: 3.48g

Explanation:

here, we will be using conservation of momentum to solve the problem. i. e the total momentum remains unchanged, unless an external force acts on the system. We'll in thus question, there is no external force acting in the system.

Remember, momentum = mass * velocity, then

mass of blood * velocity of blood = combined mass of subject and pallet * velocity of subject and pallet

Velocity of blood = 56.5cm = 0.565m

mass of blood * 0.565 = 54kg * (0.000063/0.160)

mass of blood * 0.565 = 54 * 0.00039375

mass of blood * 0.565 = 0.001969

mass of blood = 0.00348kg

Thus, the mass of blood that leaves the heart is 3.48g

Mcduff · Answer 2

Guven:

Mass of person + platform, Mt = 54 kg

= 54000 g

Velocity, Vb = 56.5 cm/s

Distance, D = 6.3 * 10^-5 m

= 6.3 * 10^-3 cm

Time = 0.16 s

V = distance/time

= 6.3 * 10^-3/0.16

= 0.039375 cm/s

From the question,

Mt * V = Mb * Vb

54000 * 0.039375 = Mb * 56.5

Calculating mass of blood,

Mb = 37.63 g

= 37.63 g of blood