A common technique used to measure the
force constant k of a spring is the following:
Hang the spring vertically, then allow a
mass m to stretch it a distance d from the
equilibrium position under the action of the
“load” m g.
Find the spring constant k if the spring
is stretched a distance 16 m by a suspended
weight of 96 N. The acceleration of gravity is
9.8 m/s^2
Answer in units of N/m.

Explanation:

Force Constant of a Spring

The force F applied to a spring produces a stretching distance x. These variables are linearly related as expressed by Hook's law:

If we could measure the distance a spring stretches when applying a known force, we'd be able to find the value of K. The experiment stated in the question places some mass of a known weight of 96 N that produced a stretching distance of 16 m. Knowing both variables, we can solve the above equation for K

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:

at positions a, g kinetic energy is maximum.

at position d, potential energy is maximum.