Question

A. Give a physical reason why the curve in the graph would not reach the vertical (Elost) axis even if the scientists had taken data over a broader range of temperatures.

b. As S increases, Elost approaches a maximum value labeled Emax on the graph above. Write an equation for Emax in terms of M, D, and physical constants, as appropriate.

Justify your answer.

c. One of the scientists, in trying to represent the relationship between the oil stiffness and the mechanical energy lost, writes down the equation 2 Elost = CS2, where C is a constant with appropriate units. Another scientist points out that this equation cannot be correct. Give two reasons why the equation cannot be correct.

Answer 1

a. The physical reason why the curve in the graph would not reach the vertical (Elost) axis even if the scientists had taken data over a broader range of temperatures is that there is always some energy loss due to friction and other factors. As temperature decreases, the oil becomes more viscous, and there is less energy loss due to friction. However, there is still some energy loss, even at very low temperatures, which prevents the curve from reaching the vertical axis.

b. The equation for Emax in terms of M, D, and physical constants is:

Emax = (π^2 * k * M) / (2 * D^2)

where k is the spring constant of the oscillator, M is the mass of the oscillator, and D is the diameter of the oscillator. This equation can be derived from the graph by finding the maximum value of Elost as S increases.

c. The equation 2 Elost = CS2 cannot be correct for two reasons. First, the units of the two sides of the equation do not match. The units of Elost are energy (Joules), while the units of CS2 are (Joules^2/m^4). Second, the equation implies that Elost is proportional to the square of the speed of the oscillator, which is not true. The energy lost by the oscillator depends on many factors, including the stiffness of the oil, the mass of the oscillator, and the amplitude of the oscillation, but it is not proportional to the square of the speed of the oscillator.

Step-by-step explanation:

hope this helps xd