NYJC_EJC 2026 Work, Energy, Power Tutorial

9814 H3 PHYSICS (2026) 1 Work, Energy and Power 1 A Level S Paper N97 Q3 Fig.1.1 shows a uniform cylindrical cork of height h and cross-sectional area A floating with its axis vertical in water of density  in a measuring cylinder. When floating, the cork displaces its own weight of water. The area of cross-section of the cylinder is only slightly- greater than A. The depth of water below the bottom of the cork is h, and the free water is h/4 above the bottom of the cork. The difference between the areas of cross-section is so small that the volume of water above the bottom of the cork is negligible. Fig. 1.1 Fig.1.2 The cork is pushed downwards slowly until it is on the base of the measuring cylinder (Fig. 1.2). Neglecting viscosity and surface tension effects, find an expression for the total work W expended in pushing the cork downwards. [6] [ 23 4 A gh ] 2 A Level S Paper N05 Q2 This question is about a simplified model of the operation of an electric fan. The blades of the fan are of length r. When the fan is rotating, it is assumed that it accelerates air from rest to velocity v. This forms a long cylinder of air of radius r moving at velocity v, as illustrated in Fig. 2.1. The density of air is . Fig. 2. (a) Obtain expressions for (i) The rate at which momentum is transferred to the air passing into the fan, [2] [ 22rv ] (ii) The magnitude of the thrust on the axle of the fan, [1] (iii) The rate at which the fan motor is working, neglecting any losses in the drive of the blades, [1] h h h h

9814 H3 PHYSICS (2026) 2 [ 23rv ] (iv) The rate at which kinetic energy is supplied to the air. [1] [ 231 2rv ] (b) The answers to (a)(iii) and (iv) should be different. Suggest one reason for this other than the losses in the drive to the blades. [1] 3 Serway 7th Ed P7.49 A particle of mass 1.18 kg is attached between two identical springs on a horizontal, frictionless table top. Both springs have spring constant k and are initially unstressed. (a) The particle is pulled a distance x along a direction perpendicular to the initial configuration of the springs as shown in the figure. Show that the force exerted by the springs on the particle is 22 ˆ21 =− −  + LF kx i xL  (b) Show that the potential energy of the system is ( ) 2 2 2( ) 2= + − +U x kx kL L x L (c) Make a plot of U(x) versus x and identify all equilibrium points. Assume L = 1.20 m and k = 40.0 Nm−1. (d) If the particle is pulled 0.500 m to the right and then released, what is its speed when it reaches the equilibrium point at x = 0? [0.823 ms−1] 4 Serway 7t