In designing circular rides for amusement parks, mechanical engineers must consider how small variations in certain parameters can alter the net force on a passenger. Consider a passenger of mass m riding around a horizontal circle of radius r at speed v . What is the variation dF in the net force magnitude for (a) a variation dr in the radius with v held constant, (b) a variation dv in the speed with r held constant, and (c) a variation dT in the period with r held constant?
In designing circular rides for amusement parks, mechanical engineers must consider how small variations in certain parameters can alter the net force on a passenger. Consider a passenger of mass m riding around a horizontal circle of radius r at speed v . What is the variation dF in the net force magnitude for (a) a variation dr in the radius with v held constant, (b) a variation dv in the speed with r held constant, and (c) a variation dT in the period with r held constant?
In designing circular rides for amusement parks, mechanical engineers must consider how small variations in certain parameters can alter the net force on a passenger. Consider a passenger of mass m riding around a horizontal circle of radius r at speed v. What is the variation dF in the net force magnitude for (a) a variation dr in the radius with v held constant, (b) a variation dv in the speed with r held constant, and (c) a variation dT in the period with r held constant?
A less than youthful 80.6 kg physics professor decides to run the 26.2 mile (42.195 km) Los Angeles Marathon. During his months of training, he realizes that one important component in running a successful marathon is carbo-loading, the consumption of a sufficient
quantity of carbohydrates prior to the race that the body can store as glycogen to burn during the race. The typical energy requirement for runners is 1 kcal/km per kilogram of body weight, and each mole of oxygen intake allows for the release of 120 kcal of energy by
oxidizing (burning) glycogen.
(a) If the professor finishes the marathon in 5:15:00 h, what is the professor's oxygen intake rate, in liters per minute, during the race if he metabolizes all of the carbo-loaded glycogen during the race and the ambient temperature is 21.5°C?
2.02
×
Read the problem statement again carefully. Is the air at standard temperature and pressure during the marathon? How would this affect the volume of 1 mol of oxygen? L/min
(b) The…
You are using a microscope to view a dust particle suspended in a drop of water on a microscope slide. As water molecules bombard the particle, it "jitters" about in a random motion (Brownian motion). The particle's average kinetic energy is the same as
3
that of a molecule in an ideal gas (K =
The particle (assumed to be spherical) has a density of 350 kg/m³ in water at 23°C.
2
BT).
(a) If the particle has a diameter d, determine an expression for its rms speed in terms of the diameter d. (Enter your answer as a multiple of d−3/2. Assume v
is in m/s and d-3/2 is in m−3/2. Do not include units in your answer.)
rms
V.
=
rms
rms
Obtain an expression for v by equating the expression for the kinetic energy of the particle in terms of v
obtain an expression for the mass of the particle in terms of its diameter. d-3/2
rms
to the expression for the average kinetic energy of a molecule. Knowing the density of the particle and assuming it is a sphere, we can
(b) Assuming the particle moves at a…
You are watching a new bridge being built near your house. You notice during the construction that two concrete spans of the bridge of total length L; = 270 m are placed end to end so that no room is allowed for expansion (figure (a)). In the opening
storyline for the thermodynamics chapter, we talked about buckling sidewalks. The same thing will happen with spans on bridges if allowance is not made for expansion (figure (b)). You want to warn the construction crew about this dangerous situation, so
you calculate the height y to which the spans will rise when they buckle in response to a temperature increase of AT = 19.0°C.
a
b
T
T+AT
y =
Ider Enter a number. made by one span, with its thermally expanded length as the hypotenuse.
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