Consider a 1kg mass at rest at the equator.Because of the earths rotation , the mass experiences a centripetal acceleration.
a)Draw free body diagram of mass
b)Find centripetal force acting in the mass
c)Compare apparent weight and true weight
d)what fictitious force would the mass experience in the earths frame?
a) To draw a free body diagram of the mass at the equator, we need to consider the forces acting on it. In this case, there are two forces acting on the mass: gravity and the centripetal force.
b) The centripetal force acting on the mass can be calculated using the formula F = m * a, where m is the mass and a is the centripetal acceleration. The centripetal acceleration can be calculated using the formula a = ω^2 * r, where ω is the angular velocity of the Earth's rotation and r is the distance from the center of the Earth to the equator. The equation for the centripetal force becomes F = m * ω^2 * r.
c) Apparent weight is the perceived weight of an object due to the forces acting on it. In this case, the apparent weight of the mass at the equator would be the combination of the force of gravity and the centripetal force. The true weight of the mass is the force due to gravity alone.
To compare the apparent weight and true weight, we need to determine the magnitude of each force. The magnitude of the apparent weight is the sum of the force of gravity and the centripetal force, while the magnitude of the true weight is just the force of gravity.
d) The fictitious force that the mass would experience in the Earth's frame is called the centrifugal force. This force is a perceived outward force experienced by objects due to the Earth's rotation. In reality, there is no actual outward force acting on the mass, but the centrifugal force is introduced to explain the observed motion from a rotating frame of reference. In the case of the mass at the equator, the centrifugal force would be equal in magnitude but opposite in direction to the centripetal force.