An unusual spring has a restoring force of magnitude F = (2.0 N/m) x + (1.0 N/m 2) x 2, where x is the stretch of the spring from its equilibrium length. A 3.00 kg mass is attached to this spring and released from rest after stretching the spring 2.00 m. What is the speed of the mass when the spring returns to its equilibrium length?

Explanation:

Given:

Equation

Force, F = (2.00 N/m)x + (1.00 N/m2)x²

Mass, m = 3 kg

Displacement, x = 2.0 m

Workdone, W = F × dx

= integrating f with respect to dx,

F = (2.00 N/m)x + (1.00 N/m2)x²

W = 2x²/2 + x^3/3

At x = 2 m,

Workdone, W = (2)^2 + (2^3)/3

= 4 + 8/3

= 20/3 J

= 6.67 J

Using conservation of energy,

Workdone, W = kinetic energy

= 1/2 × M × v^2

6.67 = 1/2 × 3 × v^2

v = sqrt(4.44)

= 2.108 m/s

adding a(n) to an electric circuit would increase the magnetic field around a wire;

b. solenoid

a solenoid is a type of electromagnet whose purpose is to generate a controlled magnetic field.

if the purpose of the solenoid is instead to impede changes in the electric current, a solenoid can be more specifically classified as an inductor rather than an electromagnet.