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
Hey, good to see you again. Here's how to solve the problem: Step 1: Convert all given values to SI units. m_1 = 300 \, g = 0.3 \, kg m_2 = 500 \, g = 0.5 \, kg a = 200 \, cm/s^2 = 2 \, m/s^2 The coefficient of friction = 0.4 and gravitational acceleration g = 9.8 \, m/s^2 are already in appropriate units. Step 2: Calculate the total mass of the system. Since the two blocks are in contact and move together, we can treat them as a single system with a total mass M. M = m_1 + m_2 = 0.3 \, kg + 0.5 \, kg = 0.8 \, kg Step 3: Calculate the total normal force acting on the blocks. On a horizontal table, the normal force N is equal to the total weight of the system. N = M · g = 0.8 \, kg × 9.8 \, m/s^2 = 7.84 \, N Step 4: Calculate the total friction force. The friction force F_f is given by the product of the coefficient of friction and the normal force. F_f = · N = 0.4 × 7.84 \, N = 3.136 \, N Step 5: Apply Newton's Second Law to find the applied force. The net force acting on the system is the applied force F_applied minus the friction force F_f. This net force causes the acceleration a. F_net = F_applied - F_f = M · a Rearrange the equation to solve for F_applied: F_applied = M · a + F_f Substitute the calculated values: F_applied = (0.8 \, kg × 2 \, m/s^2) + 3.136 \, N F_applied = 1.6 \, N + 3.136 \, N F_applied = 4.736 \, N Step 6: Round the result and compare with the given options. Rounding 4.736 \, N to two decimal places gives 4.74 \, N. This matches option C. The final answer is C. 4.74 N.