This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Welcome back ♡tasha♡....🧸 — missed you this week. Here's the solution to the problem. Given Information: Mass of body (m) = 12 kg Angle of inclination () = 30^ Coefficient of friction () = (2)/(3) Acceleration due to gravity (g) = 10 ms^-2 --- Step 1: Calculate the normal reaction force and the maximum static frictional force. The weight of the body is W = mg. W = 12 kg × 10 ms^-2 = 120 N The component of weight perpendicular to the plane is W_ = W . This is balanced by the normal reaction force R. R = W = 120 30^ = 120 × sqrt(3)2 = 60sqrt(3) N The maximum static frictional force F_f is given by F_f = R. F_f = (2)/(3) × 60sqrt(3) = 40sqrt(3) N Using sqrt(3) ≈ 1.732: F_f ≈ 40 × 1.732 = 69.28 N --- Step 2: Calculate the component of weight parallel to the plane. The component of weight parallel to the plane, acting downwards, is W_ = W . W_ = 120 30^ = 120 × (1)/(2) = 60 N --- Step 3: Find the value of P if the body is at the point of moving down the plane (a). When the body is at the point of moving down the plane, the frictional force F_f acts up the plane, opposing the impending downward motion. Since W_ (60 N) is less than F_f (69.28 N), the body would not slide down on its own. Therefore, the external force P must be acting down the plane to assist the motion. For equilibrium (point of impending motion): W_ + P = F_f P = F_f - W_ P = 40sqrt(3) - 60 P ≈ 69.28 - 60 P = 9.28 N --- Step 4: Find the value of P if the body is at the point of moving up the plane (b). When the body is at the point of moving up the plane, the frictional force F_f acts down the plane, opposing the impending upward motion. The external force P must be acting up the plane to cause this motion. For equilibrium (point of impending motion): P = W_ + F_f P = 60 + 40sqrt(3) P ≈ 60 + 69.28 P = 129.28 N Drop the next question.