A block of mass M hangs in equilibrium. the rope which is fastened to the wall is horizontal and has a tension of 38N. the rope which is fastened to the ceiling has a tension of 59N and makes an angle theta with the ceiling. what is the angle

50°

Explanation:

The tension in the rope fastened to the ceiling has horizontal component 59cosθ and its vertical component is 59sinθ. For equilibrium,

59cosθ = 38 N  (the tension in the rope attached to the wall) (1)and

59sinθ = Mg (the weight of the block of mass)  (2)

Dividing (2) by (1)

59sinθ/59cosθ = Mg/38

tanθ = Mg/38

θ = tan⁻¹(Mg/38)

Also squaring (1) and (2) and adding

(59cosθ)² = 38² N

(59sinθ)² = (Mg)²

(59cosθ)² + (59sinθ)² = 38² + (Mg)²

59²((cosθ)² + (sinθ)²) = 38² + (Mg)² . Since (cosθ)² + (sinθ)² = 1

59² = 38² + (Mg)²

Mg = √(59² - 38²) = √(3481 - 1444) = √2037 = 45.13 N

θ = tan⁻¹(Mg/38) = tan⁻¹(45.13/38) = tan⁻¹(1.1877) = 49.9° ≅ 50°

prndulum needs thread, weight clock to time swings

the answer is the first electromagnet (a). this is because it has more coils around the ferromagnetic material. increasing the number of coils increases the surface area in which the metal interacts with the current in the coil. this enables more atoms in the metal to become aligned hence becoming more magnetized.