1.)The apparent weight of a passenger in an elevator is greater than his true weight? Why is that?
2.) The radius of larger circle is twice that of a small circle. Two identical stones are attached to cords that are being whirled on a table top at the same speed. How would the tension in the longer cord related to the tension in the shorter cord be? Would it be equal?
3.) Two identical satellites are in orbbit about the earth. One orbit has a radius r, and the other 2r. the centripetal force on the satellite in the large orbit is what? is it "one fourth as great?"
Please answer these, thanks!
1. The passenger might be accelerating up or down. Just as in an elecator that is accelerating or decelerating, the apparent weight changes.
2. No, not the same. In this case the tension M V^2/R (which is the centripetal force) is inversely proportional to the string length, R. The larger circular path has half the string tension.
3. Yes (1/4), because of the inverse square law of gravitationa attraction between the earth and the satellite.
thank you for answering this and the other one
T1=.5T2
1.) The apparent weight of a passenger in an elevator is greater than his true weight due to the effect of upward or downward acceleration. When the elevator is accelerating upward or downward, the passenger experiences a sensation of being pushed into the floor or lifted off the floor. This sensation is also referred to as the "force of inertia" or "apparent weight."
To understand why the apparent weight is greater, we need to consider Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration. In an elevator, when it is accelerating upward, the force experienced by the passenger is the sum of his true weight (gravity pulling him downward) and the force of inertia (accelerating upward). Mathematically, this can be expressed as:
Apparent weight = True weight + Force of inertia
Since acceleration is involved, the force of inertia is proportional to the passenger's mass and the elevator's acceleration. Hence, the apparent weight is increased compared to the true weight of the passenger.
2.) When two identical stones attached to cords are whirled on a tabletop, the tension in the longer cord is greater than the tension in the shorter cord.
To understand why the tension is different, we can consider the concept of centripetal force. Centripetal force is the force that acts towards the center of a circular path and keeps an object moving in a circle.
The centripetal force required for an object to move in a circle depends on its mass and the radius of the circle. When an object is twirled in a larger circle, the radius of the circle is larger. According to the equation for centripetal force (F = (m*v^2) / r), if the mass and velocity of both stones are the same, the tension in the cords will be directly proportional to the square of the velocity and inversely proportional to the radius.
Since the radius of the larger circle is twice that of the smaller circle, the tension in the longer cord will be four times greater than the tension in the shorter cord.
3.) The centripetal force on the satellite in the larger orbit is one-fourth as great as the centripetal force on the satellite in the smaller orbit.
The centripetal force required for an object to stay in orbit is provided by the gravitational force between the object and the planet it is orbiting. The gravitational force is given by Newton's law of universal gravitation, which states that the force is proportional to the masses of the objects involved and inversely proportional to the square of the distance between them.
In this scenario, we have two identical satellites in orbit around the Earth, with one orbit having a radius of r and the other having a radius of 2r. When comparing the centripetal forces, we need to consider the effect of the radius on the gravitational force.
As per the inverse square relationship, doubling the radius will result in the gravitational force being reduced to one-fourth of its original value. This means that the centripetal force required for the satellite in the larger orbit will also be reduced to one-fourth as great as the centripetal force for the satellite in the smaller orbit.