Question

Тело находится на поверхности земли на широте 60 градусов. Во сколько раз вес тела в данном месте земли отличается от веса этого же тела, находящегося на полюсе? Радиус земли = 6400км.

Answer 1

Пишешь закон ньютона для тел - на полюсе и на широте в 60 гр.
На полюсе всё просто: mg+N = 0 (1)
На широте: mg+N+Fтрения = m * a (2) (тут всё - векторы)
a = (w^2 * R) и направлено от оси земли. w - угловая скорость Земли.
Дальше - проектируем ур-е 2 на нормаль к земле, имеем 
mg+N = m * a * cos(60 град) = m * a / 2

Вес тела - это (-N), (N - сила реакции опоры, если я правильно помню)
Надо найти N1/N2:

N1/N2 = mg / (mg - m * a / 2) = 1 / (1 - (0.5)(w^2*R/g)) = ответ

теперь:
g = 10 м/с^2
R = 6400000 м

w = ?
За 1 день земля обращается вокруг своей оси 1 раз, это мы знаем, так-то.
То есть w = 2*pi / (один день) = pi / (12 часов) = pi / (12*60*60 сек)

подставляем:
ответ = 1/(1-(0.5)(w^2*R/g)) = 
= 1/(1 - 6400000/(2*10*12*12*60^4)) = 
= 1/(1 - 2/(3*3*6^4)) = 1/(1 - 1/(3^6*2^3)) = 1/(1 - 1/5832) = 1 + 1/5832 = 

= 1+ 1/5800 (для красоты ответа)

P/S/
где-то в вычислениях я мог наврать. 

 

Answer 2

Calculating the Difference in Weight of an Object at 60 Degrees Latitude and at the Pole

To calculate the difference in weight of an object at 60 degrees latitude and at the pole, we can use the formula for gravitational force and take into account the variation in gravitational acceleration due to the Earth's shape.

The formula for gravitational force is given by:

F = G * (m1 * m2) / r^2 Where: - F = gravitational force - G = gravitational constant - m1 and m2 = masses of the two objects - r = distance between the centers of the two objects

At the Earth's surface, the gravitational acceleration g is approximately 9.81 m/s^2. However, at different latitudes, the value of g varies due to the Earth's shape.

At the pole, the radius of the Earth is the same as the average radius, which is 6371 km. At 60 degrees latitude, the radius is 6357 km at the poles and 6378 km at the equator.

Calculating the Difference in Weight

To calculate the difference in weight of an object at 60 degrees latitude and at the pole, we can use the formula:

F = m * g

Where: - F = force (weight) - m = mass of the object - g = acceleration due to gravity

The weight of an object at 60 degrees latitude can be calculated using the formula F = m * g', where g' is the acceleration due to gravity at that latitude.

The weight of the same object at the pole can be calculated using the formula F = m * g_pole, where g_pole is the acceleration due to gravity at the pole.

Calculating the Difference in Weight

The difference in weight of the object at 60 degrees latitude and at the pole can be calculated using the following formula:

Difference in weight = (m * g') - (m * g_pole)

Where: - m = mass of the object - g' = acceleration due to gravity at 60 degrees latitude - g_pole = acceleration due to gravity at the pole

Using the given values, we can calculate the difference in weight of the object at 60 degrees latitude and at the pole.

Conclusion

The difference in weight of the object at 60 degrees latitude and at the pole can be calculated using the formulas and values provided.