Final answer:
The angle ϕ is approximately 44.7°.
Step-by-step explanation:
To find the angle ϕ, we can start by analyzing the forces acting on the physics textbook. The tension in the rope is equal to the weight of the book component along the slope. The weight component acting parallel to the slope is given by mg sin(ϕ), where m is the mass of the book. Therefore, we can write the equation:
Tension = mg sin(ϕ)
Substituting the given values, we have:
14.0 N = 2.0 kg * 9.8 m/s^2 * sin(ϕ)
Solving for ϕ, we find:
sin(ϕ) = 14.0 N / (2.0 kg * 9.8 m/s^2)
sin(ϕ) = 0.7143
ϕ ≈ sin^{-1}(0.7143)
ϕ ≈ 44.7°