The vernal equinox and the autumnal equinox are associated with two points 180° apart in the Earth’s orbit. That is, the Earth is on precisely opposite sides of the Sun when it passes through these two points. From the vernal equinox. 185.4 days elapse before the autumnal equinox. Only 179.8 days elapse from the autumnal equinox until the next vernal equinox. Why is the interval from the March (vernal) to the September (autumnal) equinox (which contains the summer solstice) longer than the interval from the September to the March equinox rather than being equal to that interval? Choose one of the following reasons, (a) They are really the same, but the Earth spins faster during the “summer” interval, so the days are shorter, (b) Over the “summer” interval, the Earth moves slower because it is farther from the Sun. (c) Over the March-to-September interval, the Earth moves slower because it is closer to the Sun. (d) The Earth has less kinetic energy when it is warmer, (e) The Earth has less orbital angular momentum when it is warmer.
The vernal equinox and the autumnal equinox are associated with two points 180° apart in the Earth’s orbit. That is, the Earth is on precisely opposite sides of the Sun when it passes through these two points. From the vernal equinox. 185.4 days elapse before the autumnal equinox. Only 179.8 days elapse from the autumnal equinox until the next vernal equinox. Why is the interval from the March (vernal) to the September (autumnal) equinox (which contains the summer solstice) longer than the interval from the September to the March equinox rather than being equal to that interval? Choose one of the following reasons, (a) They are really the same, but the Earth spins faster during the “summer” interval, so the days are shorter, (b) Over the “summer” interval, the Earth moves slower because it is farther from the Sun. (c) Over the March-to-September interval, the Earth moves slower because it is closer to the Sun. (d) The Earth has less kinetic energy when it is warmer, (e) The Earth has less orbital angular momentum when it is warmer.
Solution Summary: The author explains that Earth's orbit radius is smallest in January during the winters and longest in July, during summers.
The vernal equinox and the autumnal equinox are associated with two points 180° apart in the Earth’s orbit. That is, the Earth is on precisely opposite sides of the Sun when it passes through these two points. From the vernal equinox. 185.4 days elapse before the autumnal equinox. Only 179.8 days elapse from the autumnal equinox until the next vernal equinox. Why is the interval from the March (vernal) to the September (autumnal) equinox (which contains the summer solstice) longer than the interval from the September to the March equinox rather than being equal to that interval? Choose one of the following reasons, (a) They are really the same, but the Earth spins faster during the “summer” interval, so the days are shorter, (b) Over the “summer” interval, the Earth moves slower because it is farther from the Sun. (c) Over the March-to-September interval, the Earth moves slower because it is closer to the Sun. (d) The Earth has less kinetic energy when it is warmer, (e) The Earth has less orbital angular momentum when it is warmer.
Definition Definition Product of the moment of inertia and angular velocity of the rotating body: (L) = Iω Angular momentum is a vector quantity, and it has both magnitude and direction. The magnitude of angular momentum is represented by the length of the vector, and the direction is the same as the direction of angular velocity.
5.48 ⚫ A flat (unbanked) curve on a highway has a radius of 170.0 m.
A car rounds the curve at a speed of 25.0 m/s. (a) What is the minimum
coefficient of static friction that will prevent sliding? (b) Suppose that the
highway is icy and the coefficient of static friction between the tires and
pavement is only one-third of what you found in part (a). What should
be the maximum speed of the car so that it can round the curve safely?
5.77 A block with mass m₁ is placed on an inclined plane with
slope angle a and is connected to a hanging block with mass m₂ by a
cord passing over a small, frictionless pulley (Fig. P5.74). The coef-
ficient of static friction is μs, and the coefficient of kinetic friction is
Mk. (a) Find the value of m₂ for which the block of mass m₁ moves up
the plane at constant speed once it is set in motion. (b) Find the value
of m2 for which the block of mass m₁ moves down the plane at constant
speed once it is set in motion. (c) For what range of values of m₂ will
the blocks remain at rest if they are released from rest?
5.78 .. DATA BIO The Flying Leap of a Flea. High-speed motion
pictures (3500 frames/second) of a jumping 210 μg flea yielded the
data to plot the flea's acceleration as a function of time, as shown in
Fig. P5.78. (See "The Flying Leap of the Flea," by M. Rothschild et al.,
Scientific American, November 1973.) This flea was about 2 mm long
and jumped at a nearly vertical takeoff angle. Using the graph, (a) find
the initial net external force on the flea. How does it compare to the
flea's weight? (b) Find the maximum net external force on this jump-
ing flea. When does this maximum force occur? (c) Use the graph to
find the flea's maximum speed.
Figure P5.78
150
a/g
100
50
1.0
1.5
0.5
Time (ms)
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