a 3.5kg child is swinging on a rope. the length of the rope attached to a tree branch is 7.00m. ths child passes through the lowest point of the curved path with a speed of 3.00m/s. what is the tension on the rope at this moment

The child's radial/centripetal acceleration at the lowest point of the swing is

a = (3.00 m/s)² / (7.00 m) = 1.29 m/s²

By Newton's second law, the tension in the rope is

T = (3.5 kg) (1.29 m/s²) = 4.5 N

(Does the question really say the child's mass is 3.5 kg? That's little more than the average mass of a newborn, about 3.3 kg. Not exactly a good idea to put a newborn on a swinging rope...)

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.