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
To calculate the speed of the stone, we'll first find the elastic potential energy stored in the stretched catapult and then equate it to the kinetic energy of the stone. Step 1: Calculate the elastic potential energy stored in the catapult. The energy stored in the catapult is equal to the work done to stretch it. Given: Average force, F_avg = 70 N Distance stretched, x = 7 cm = 0.07 m The elastic potential energy (U) is: U = F_avg × x U = 70 N × 0.07 m U = 4.9 J Step 2: Apply the principle of conservation of energy. When the stone is released, the elastic potential energy stored in the catapult is converted into the kinetic energy of the stone. U = K Where K is the kinetic energy of the stone, given by K = (1)/(2) m v^2. Given: Mass of stone, m = 5 g = 0.005 kg So, we have: 4.9 J = (1)/(2) m v^2 4.9 = (1)/(2) (0.005) v^2 Step 3: Solve for the speed (v) of the stone. 4.9 = 0.0025 v^2 v^2 = (4.9)/(0.0025) v^2 = 1960 v = sqrt(1960) v ≈ 44.27 m/s The speed of the stone at the time of release is approximately 44.27 m/s. The final answer is 44.27 m/s What's next?