A merry-go-round with a a radius of R = 1.63 m and moment of inertia I = 196 kg-m2 is spinning with an initial angular speed of
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Answer:
(A) The tension's magnitude grows to four times the initial value, 4F.
Explanation:
When an object travels in a circular path, a centripetal force is exerted upon it. In this instance, the centripetal force acting on the stone can be represented by .
Here, m denotes the mass of the object
v is the velocity or speed of the object
r signifies the radius of the circular path
Importantly, the tension corresponds to the centripetal force.
Initially, the string completes one revolution each second, and subsequently, it accelerates to perform two revolutions in the same time frame. This signifies that the speed has increased twofold.
Applying our formula:F =
where F indicates the tension in the string
assuming the starting speed is v, after doubling it becomes 2v
Maintaining the circle's radius, we arrive at:
F=
From this equation, it's clear that the initial tension has quadrupled.
Consequently, the magnitude of the tension increases to four times its original value, 4F.
Para calcular el peso utilizamos la fórmula:
Cuando tenemos dos cuerpos, empleamos la fórmula de la gravedad general:
Donde:
G = constante de gravedad =
Mp = masa de la persona = 882 / 9.81= 89.9kg
ME = masa de la Tierra =
r = distancia entre la Tierra y la persona
A partir de estas dos fórmulas, deducimos que los lados izquierdos son equivalentes, por lo tanto, los lados derechos también deben serlo.
Resolviendo esta ecuación para r:
r=6371116m = 6371.116km
Esta es la distancia desde el centro de la Tierra. El radio de la Tierra es 6370km y la altura sobre la superficie es 6371.116 - 6370 = 1.116km o 1116m.