A wooden block with a mass of 1.30 kg is placed against a compressed spring at the bottom of a slope inclined at an angle of 25.0 circ with the horizontal (refer to this as location A).

Part A: The change in gravitational potential energy can be found using the formula: ?PE = mgh where ?PE is the change in gravitational potential energy, m is the mass of the block, g is the acceleration due to gravity, and h is the change in height (the vertical distance between points A and B). We can find h by using trigonometry: h = sin(25°) x 7.20 m = 3.08 m Substituting the values into the formula, we get: ?PE = (1.30 kg) x (9.81 m/s?) x (3.08 m) = 38.8 J Therefore, the change in gravitational potential energy for the system of the block and the Earth as the block moves from point A to point B is 38.8 J. Part B: The amount of thermal energy produced can be found using the formula: Q = ?kN?d where Q is the thermal energy produced, ?k is the coefficient of kinetic friction, N is the normal force, and ?d is the distance traveled. We can find N by resolving the weight of the block into components: N = mg cos(25°) = (1.30 kg) x (9.81 m/s?) x cos(25°) = 11.8 N And we can find ?d by using trigonometry again: ?d = cos(25°) x 7.20 m = 6.49 m Substituting the values into the formula, we get: Q = (0.50) x (11.8 N) x (6.49 m) = 41.6 J Therefore, the thermal energy produced in the block and the slope as the block moves from point A to point B is 41.6 J. Part C: The amount of potential energy initially stored in the spring can be found using the formula: PE = (1/2)kx? where PE is the potential energy stored in the spring, k is the spring constant, and x is the distance the spring is compressed. We assume that the spring potential energy is zero when the spring is relaxed, so x is the initial compression of the spring. We do not know k, but we can use the measured speed of the block at point B to find its kinetic energy, and then use the conservation of energy to relate it to the initial potential energy stored in the spring: KE = (1/2)mv? where KE is the kinetic energy of the block at point B, m is the mass of the block, and v is the speed of the block at point B. Substituting the values given in the problem, we get: KE = (1/2) x (1.30 kg) x (7.00 m/s)? = 32.2 J Using the conservation of energy, we know that the initial potential energy stored in the spring is equal to the sum of the final kinetic energy of the block and the work done by non-conservative forces (due to friction). We already know the final kinetic energy, and we can find the work done by non-conservative forces using the formula: W = ?kN?d where W is the work done by non-conservative forces, ?k is the coefficient of kinetic friction, and ?d is the distance traveled. We can use the same values of ?k, N, and ?d as in Part B to find W: W = (0.50) x (11.8 N) x (6.49 m) = 38.0 J Therefore, the initial potential energy stored in the spring is: PE = KE + W = 32.2 J + 38.0 J = 112 J Therefore, the amount of potential energy initially stored in the spring is 112 J. Part D: The work done by non-conservative forces is equal to the thermal energy produced, which we found to be 41.6 J in Part B. The change in mechanical energy of the block-Earth system is equal to the change in gravitational potential energy plus the work done by non-conservative forces. We found the change in gravitational potential energy to be 38.8 J in Part A. Therefore: W(non-conservative) = 41.6 J change in energy = 38.8 J + 41.6 J = 80.4 J Therefore, the ordered pair is (41.6 J, 80.4 J).