An early major objection to the idea that the earth rotates on its axis was that it would have
to turn so fast that people would be thrown off into space. Show the error in this logic by
calculating:
the speed of a 100 kg person standing at the equator. (The radius of the earth is
about 6400 km).
v = 2πrf = 2π * 6400km * 1/24hr = 1675.5 km/hr = 465.4 m/s
Thanks but how do I do this ?
b. the net force necessary to keep the person in this motion.
c. how the normal force acting on the person compares to their weight.
d. From your answers to these questions, explain why people do not fly off into
space. What would happen to the size of the normal force if the earth spun faster?
To calculate the speed of a person standing at the equator, we can use the formula for the linear speed of a rotating object:
v = rω
Where:
v is the linear speed,
r is the radius of rotation (in this case, the radius of the Earth),
and ω is the angular speed, which represents the rate of rotation.
The angular speed ω can be calculated using the formula:
ω = 2π/T
Where:
T is the time taken for one complete rotation, which is approximately 24 hours or 86400 seconds.
First, we need to convert the radius of the Earth from kilometers (km) to meters (m):
radius = 6400 km = 6400 * 1000 m = 6,400,000 m
Now, let's calculate the angular speed ω:
ω = 2π / T
= 2π / 86400 s
Next, we can calculate the linear speed v using the formula v = rω:
v = (6,400,000 m) * (2π / 86400 s)
Simplifying the calculation:
v ≈ 464.1 m/s
Therefore, the speed of a 100 kg person standing at the equator is approximately 464.1 meters per second.
To calculate the speed of a person standing at the equator, we need to know the time it takes for the Earth to complete one rotation on its axis.
The time it takes for the Earth to complete one rotation is approximately 24 hours, or 86,400 seconds. This means that the Earth rotates 360 degrees in 86,400 seconds.
To calculate the speed of a person standing at the equator, we need to find the distance traveled by a point on the equator in that time. The distance traveled by a point on the equator is equal to 2π times the radius of the Earth (since the equator is a circle), which is approximately 40,075 kilometers.
Now, we can calculate the speed using the formula:
Speed = Distance / Time
Speed = 40,075 km / 86,400 s
Let's convert the units to make the calculation easier:
Speed = 40,075,000 m / 86,400 s
Speed ≈ 463.02 m/s
Therefore, the speed of a 100 kg person standing at the equator is approximately 463.02 meters per second. This speed is much higher than what we experience in our everyday lives, but it is not fast enough to throw us off into space.