Use the general formulas for gravitational force and centripetal force to derive the relationship between speed and orbital radius for circular objects. the centripetal force is provided by gravity. set formulas equal to each other and solve for velocity

Explanation:

The universal law of gravitation is defined as:

 (1)                

Where G is the gravitational constant, M and m are the masses of the two objects and r is the distance between them.

The centripetal force can be found by means of Newton's second law:

 (2)

Since it is a circular motion, the acceleration can be defined as:

 (3)

Where v is the velocity and r is the orbital radius.

Replacing equation (3) in equation (2) it is gotten:

 (4)

Hence,

Then, v can be isolated:

So the relationship between speed and orbital radius is given by the expression

carla slowed down in the beginning of her trip, stopped, and then sped up

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation: