A device used since the 1940 s to measure the kick or recoil of the body due to heart beats is the “ballistocardiograph.” What physics principle(s) are involved here to measure the force of cardiac contraction? How might we construct such a device?
The ballistocardiograph works on the principles of impulsive force and conservation of momentum, which are the consequences of Newton’s second and third laws of motion, respectively.
A force that acts on a body for a short period of time is called cardiac contraction force. An impulsive force is the name for this type of force. This force is defined as the ratio of momentum change to time interval.
Here, Pi = 0 is the force, is the change in momentum and is the time interval. This is a consequence of Newton’s second law of motion. The time interval is equal to the pulsation time, and you need to calculate the rate of change of momentum.
As per Newton's third law of motion, momentum is conserved in the body. Momentum is the product of mass and velocity. The initial momentum will be zero because the body is immobile.
Pi = 0
The final momentum is equal to the sum of the momentum of the heart pump and the momentum of the body that recoils in the direction opposite to the heart pump.
Here, m is the mass of blood, M is the mass of the body, v1 is the velocity of blood and v2 is the velocity of body. Therefore, change in momentum is calculated as follows:
Substitute this value in the expression of force.Thus, the force can be calculated.
The ballistocardiograph can be constructed by taking a highly mobile table that is capable of sensing the movements of the body that is placed on the table, and the recording system can be attached to it. It gives the frequency at which the heart beats.
Therefore, the ballistocardiograph works on the principle of Newton’s second and third laws of motion.
(a) Give an example of different net external forces acting on the same system to produce different accelerations. (b) Give an example of the same net external force acting on systems of different masses, producing different accelerations. (c) What law accurately describes both effects? State it in words and as an equation.
(a) What is the strength of the weak nuclear force relative to the strong nuclear force?
(b) What is the strength of the weak nuclear force relative to the electromagnetic force?
Since the weak nuclear force acts at only very short distances, such as inside nuclei, where the strong and electromagnetic forces also act, it might seem surprising that we have any knowledge of it at all. We have such knowledge because the weak nuclear force is responsible for beta decay, a type of nuclear decay not explained by other forces.
(a) Calculate the tension in a vertical strand of spider web if a spider of mass 8.00×10−5 kg hangs motionless on it.
(b) Calculate the tension in a horizontal strand of spider web if the same spider sits motionless in the middle of it, much like the tightrope walker in Figure 4.17. The strand sags at an angle of 12º below the horizontal. Compare this with the tension in the vertical strand (find their ratio).
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