HCI 05 WEP Solutions (Discussion Questions)

Topic 5 Work Energy Power Suggested Solutions to Discussion Questions Qn Ans Explanation D1 [2008/P3/Q1(part)] F = gradient of W-d graph, W = area under F-d graph, From d = 0 to 1.0 m, W increases linearly (as F is positive & constant), from 0 to 1.0 x 5.0 = 5.0 J From d =1.0 to 2.0 m, W increases at increasing rate (as F is positive & increasing), from 5.0 to [5.0 + (½)(15)(1.0)] = 17.5 J From d = 2.0 to 3.0 m, W increases linearly (as F is positive & constant), from 17.5 J to [17.5 + 1.0(20)] = 37.5 J From d = 3.0 to 4.0 m, W increase at decreasing rate (as F is positive & decreasing), from 37.5 J to [37.5 + (½)(1.0)(2.0)] = 47.5 J D2 C [CIE June 2003] There is no change in kinetic energy, since the trolley starts and finishes at rest, so the weight is only gaining gravitational potential energy. work done by tension force (trolley) PE mg h Wq    To better appreciate and understand the situation, one possible scenario is as shown in the F- x graphs. Tension force, T is a varying force, weight mg acts in opposite direction. Comparing the area under each graph, positive work done by T = negative work done by mg Total work done = work done by net force Fnet = 0 J thus, satisfying the condition that the weight is lifted from rest and finishes at rest with no change in KE.

D3 C F = -dU/dx or the negative of the gradient of U-x graph. The force on the body is the negative gradient of the potential energy-position graph. Since the gradient of the graph is positive and constant, the force is negative and constant, implying that the force acts in the opposite direction to the displacement. In other words, the force acts towards the origin, in the direction towards lower potential energy. D4 E F = -dU/dx The force between the molecules is the negative of the gradient of the potential energy (of the 2 molecules)-distance graph. When x < r2, the gradient of tangent line at a point on the graph is negative, the intermolecular force is thus positive (in the direction of +x), it is repulsive. When x > r2, the gradient of tangent line at a point on the graph is positive, the intermolecular force is negative (in the opposite direction to +x), it is attractive. Further reference: https://www.schoolphysics.co.uk/age16-19/Properties%20of%20matter/Elasticity/text/Intermolecular_forces/index.html D5 D [H1 N2009/P1/Q6 & 2015 P1 Q11] Recall Work done by a force = area under the force-displacement graph. Hence option D is correct. As for option A, work done by F is equal to elastic potential energy stored in the wire only when the wire is within its elastic limit. Since the wire is stretched beyond its elastic limit, (as seen on the left) not all work done by F becomes elastic pot ential energy, t he energy is lost and cannot be recovered when releasing the load. D6 C [H1 2010/P1/Q11] Area under graph from x = 0 to extension up to point Q = ∫Fdx whi