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 find the work done by the non-conservative force, we can use the Work-Energy Theorem, which states that the work done by non-conservative forces (W_nc) is equal to the change in the total mechanical energy ( E_mech). The change in mechanical energy is the sum of the change in kinetic energy ( KE) and the change in gravitational potential energy ( PE_g). Since the problem states the incline is "smooth," there is no friction. The non-conservative force F_nc is the only non-conservative force acting. The problem does not specify any initial or final velocity, so we assume the block starts from rest at the bottom and ends at rest at the top, meaning the change in kinetic energy is zero ( KE = 0). Step 1: Identify the given values. Mass of the block, m = 2 kg Height of the incline, h = 5 m Acceleration due to gravity, g = 9.8 m/s^2 (standard value) Length of the incline, d = 10 m (This value is not directly needed for this approach, but it's consistent with the height.) Step 2: State the Work-Energy Theorem for non-conservative forces. W_nc = E_mech = KE + PE_g Step 3: Calculate the change in kinetic energy ( KE). Assuming the block starts and ends at rest: v_i = 0 m/s v_f = 0 m/s KE = (1)/(2)mv_f^2 - (1)/(2)mv_i^2 = (1)/(2)m(0)^2 - (1)/(2)m(0)^2 = 0 J Step 4: Calculate the change in gravitational potential energy ( PE_g). The block is pulled up from a height of 0 m to 5 m. PE_g = mgh_f - mgh_i = mg(h) - mg(0) PE_g = mgh PE_g = (2 kg)(9.8 m/s^2)(5 m) PE_g = 98 J Step 5: Calculate the work done by the non-conservative force (W_nc). W_nc = KE + PE_g W_nc = 0 J + 98 J W_nc = 98 J The work done by the non-conservative force is 98 J. What's next?