See attached file for the diagram.
1. The diagram shows the acceleration of blood in the vasculature versus time in seconds. Give the time at which the blood is moving with the maximum velocity. Explain your answer.
2. All modern elevators feature safety mechanisms. For example, if an elevator cable breaks, the falling elevator car will land on a set of giant springs on the bottom of the shaft, compressing them. However, the conservation of energy asserts that the energy required to break the car's fall is the same whether the springs are present or not. How, then, do the springs save lives? (Be specific - what quantities are changed when the springs are present? Which of these explains the difference?)© BrainMass Inc. brainmass.com December 24, 2021, 9:37 pm ad1c9bdddf
SOLUTION This solution is FREE courtesy of BrainMass!
1. Acceleration a = dv/dt.
Velocity v = Integral of adt = Area under the curve for a given infinitesimally small time duration
Hence, velocity of blood at any given instant is given by the area under the a vs t graph.
Let us take a time duration of 1 sec and see at which second the area under the given graph in maximum. It is obvious that the area under the graph is maximum during the 2nd second. Hence, speed of the blood is maximum during 2nd second.
2. As the elevator car falls to the ground freely, its velocity (hence KE) goes on increasing at the cost of its potential energy which goes on decreasing. By the time the car reaches the ground, it has acquired a very large momentum. If the car hits the hard ground, its momentum reduces to zero instantly (or in an extremely small duration). By Newton's second law of motion we have Force F = d(mv)/dt. As the momentum reduces from a large magnitude to zero in a very short duration, the rate of change of momentum has a very large magnitude which in turn results in generation of a very large impulsive force on the car (and in turn passengers). This large force could be very dangerous for the passengers resulting in serious injury or fatality.
In case the car lands on a huge spring, the spring gets compressed and brings about stoppage of the car gradually, over a longer time duration resulting in significantly lesser rate of change of momentum and consequently lesser magnitude of destructive forces on the passengers.
To summarize: with the springs present, the rate of change of momentum (hence the force generated) is much less in magnitude as compared to landing directly on the ground.© BrainMass Inc. brainmass.com December 24, 2021, 9:37 pm ad1c9bdddf>