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
Step 1: Convert given values to SI units for Question 3. Mass m = 20 g = 20 × 10^-3 kg = 0.02 kg Extension x = 4 cm = 4 × 10^-2 m = 0.04 m Force constant k = 200 Nm^-1 Step 2: Apply the principle of conservation of energy for Question 3. The elastic potential energy stored in the rubber is converted into the kinetic energy of the stone. E_p = E_k (1)/(2)kx^2 = (1)/(2)mv^2 Step 3: Substitute the values and solve for velocity v for Question 3. (1)/(2)(200 Nm^-1)(0.04 m)^2 = (1)/(2)(0.02 kg)v^2 (200)(0.0016) = (0.02)v^2 0.32 = 0.02v^2 v^2 = (0.32)/(0.02) v^2 = 16 v = sqrt(16) v = 4 m/s The velocity with which the stone leaves the catapult is 4 m/s. Step 4: Identify given values for Question 4. Compression x = 0.02 m Force constant k = 400 Nm^-1 Step 5: Calculate the energy stored in the spring for Question 4. The energy stored in a spring is given by the elastic potential energy formula: E_p = (1)/(2)kx^2 E_p = (1)/(2)(400 Nm^-1)(0.02 m)^2 E_p = (1)/(2)(400)(0.0004) E_p = 200(0.0004) E_p = 0.08 J The energy stored in the spring is 0.08 J. Send me the next one 📸