Two objects slide without friction on a circular ring of radius r oriented in a vertical plane. the heavier object (of mass 3m) is attached to a spring with an unstretched length of zero (admittedly an unphysical assumption) and spring constant k. the fixed end of the spring is attached to a point a horizontal distance 2r from the center of the circle. the lighter object (of mass m) is initially at rest at the bottom of the ring. the heavier object is released from rest at the top of the ring, then collides with and sticks to the lighter object. find the value for m that will allow the combined object (of mass 4m) to just reach the point a on the ring, but go no higher. express your answer in terms of some or all of the quantities k, r and the acceleration of gravity g.

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:

probably not if net force is zero

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2