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.
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5.1 State the principle of conservation of mechanical energy in words. The principle of conservation of mechanical energy states that the total mechanical energy (sum of kinetic and potential energy) of an isolated system remains constant if only conservative forces do work on the objects within the system. 5.2 Is the mechanical energy of the object CONSERVED or NOT CONSERVED while the object is moving from point P to point Q along the horizontal surface? Give a reason for the answer. NOT CONSERVED. This is because a non-conservative force (friction) does work on the object as it moves from P to Q. 5.3 Calculate the: 5.3.1 Magnitude of the angle , shown in the diagram above, using energy principles ONLY. Step 1: Identify the initial and final states and the forces doing work. Initial state (P): v_P = 0 m/s, h_P = 0 m. Final state (R): v_R = 0 m/s, h_R = 40 cm = 0.4 m. Forces doing work from P to R: applied force F, frictional force f_k, and gravitational force F_g. Step 2: Apply the Work-Energy Theorem from point P to point R. The Work-Energy Theorem states that the net work done on an object equals its change in kinetic energy: W_net = K. Since the object starts from rest at P and stops at R, K = K_R - K_P = 0 - 0 = 0. Therefore, W_net = 0. The net work is the sum of the work done by all forces: W_net = W_F + W_friction + W_g W_F = F x W_friction = f_k x 180^ = -f_k x W_g = -mgh_R Note: The applied force F and frictional force f_k only act from P to Q. The gravitational force F_g does work over the vertical displacement from Q to R. Step 3: Substitute the known values into the Work-Energy Theorem equation. Given: F = 80 N x = 4 m (distance from P to Q) f_k = 45 N m = 20 kg g = 9.8 m/s^2 h_R = 0.4 m F x - f_k x - mgh_R = 0 (80 N)(4 m) - (45 N)(4 m) - (20 kg)(9.8 m/s^2)(0.4 m) = 0 320 - 180 - 78.4 = 0 320 - 258.4 = 0 320 = 258.4 = (258.4)/(320) = 0.8075 = (0.8075) ≈ 36.13^ The magnitude of the angle is 36.13^. 5.3.2 Power delivered by force F if the time taken for the object to move from point P to point Q is 2.86 seconds. Step 1: Calculate the work done by force F from P to Q. W_F = F x Using the value of from 5.3.1: W_F = (80 N)(4 m) (36.13^) W_F = 320 (36.13^) W_F = 320 × 0.8075 W_F = 258.4 J Step 2: Calculate the power delivered by force F. Power P is defined as the rate at which work is done: P = (W_F)/(t) Given t = 2.86 s: P = 258.4 J2.86 s P ≈ 90.35 W The power delivered by force F is 90.35 W. That's 2 down. 3 left today — send the next one.