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
Another one Hurry — let's solve it. a) velocity of the box after sliding 6\, m from the starting point; Step 1: Determine the acceleration of the box down the smooth inclined plane. The component of gravitational force acting parallel to the incline causes the acceleration. a = g Given g = 10\, m/s^2 and = 30^: a = 10\, m/s^2 × (30^) a = 10\, m/s^2 × 0.5 a = 5\, m/s^2 Step 2: Use a kinematic equation to find the final velocity. The box starts from rest, so initial velocity u = 0\, m/s. The distance slid is s = 6\, m. Using the equation v^2 = u^2 + 2as: v^2 = (0\, m/s)^2 + 2(5\, m/s^2)(6\, m) v^2 = 0 + 60\, m^2/s^2 v = sqrt(60)\, m/s v ≈ 7.74596\, m/s Correct to one decimal place: v = 7.7\, m/s b) momentum of the box 6\, m from the starting point. Step 1: Calculate the momentum using the mass and the velocity found in part (a). Momentum p = mv. Given mass m = 20\, kg and velocity v = sqrt(60)\, m/s: p = 20\, kg × sqrt(60)\, m/s p ≈ 20\, kg × 7.74596\, m/s p ≈ 154.9192\, kg m/s Correct to one decimal place: p = 154.9\, kg m/s Drop the next question.