NJC 04P Energy & Fields Problem Set 2025

National Junior College Science Department | Physics 4. Energy & Fields Problem Set 4.1 ENERGY STORES AND TRANSFERS 4.1.1 Exercises For this section of the problem set, you should try the exercises without looking at the solutions. The solutions are there if you get stuck and you should also use it to understand how to present your work. E1 An arrow is placed on the string of a bow and pulled back before being released from the bow. Describe the energy stores and transfers of the arrow. 4.1.2 Problem P1. N12/1/10 The top end of a spring is attached to a fixed point and a mass of 4.2 kg is attached to its lower end. The mass is released and after bouncing up and down several times it comes to rest at a distance 0.29 m below its starting point. Which row gives the gain in the gravitational potential energy of the mass Ep and the gain in the elastic potential energy of the spring Es? Ep / J Es / J A –12 +12 B –12 +6 C +12 +12 D +12 +6 4.2 WORK DONE BY A FORCE 4.2.1 Exercises E2 (a) Calculate the work done by Denise to drag her basket of laundry of mass 5.0 kg a distance of 5.0 m along a floor, if the force she exerts is 30.0 N at an angle of 60° with the horizontal. [75 J] (b) Hilda holds a gardening book of weight 10 N at a height of 1.0 m above her patio for 50s. Calculate the work done by Hilda during the 50 s? [0 J]

National Junior College Science Department | Physics E3 (a) Can work done be positive or negative? State the condition for it. (b) Can work done be zero? State the condition(s) for it. E4 An object at rest is pulled by a constant horizontal force, F on a smooth floor to a displacement of x. (a) Sketch a graph of force applied on object against the displacement. Label F and x in the graph. (b) What does the area under force against displacement graph in (i) represent? E5 An object at rest is pulled by a varying horizontal force, Fx on a smooth floor to a displacement of x. (a) Can we still use this formula to calculate the work done by Fx, i.e workdone = Fx(x)? (b) How can the work done by Fx be calculated? 4.2.2 Problems P2. 2011/P1/Q11 A constant force F is applied to a stationary object of mass m on a frictionless surface. A constant acceleration increases the velocity of the object to some value v in a time t. It covers a distance s during this time. Which value of energy is given to the object’s kinetic store? A Fst B Fv C Fs D 2 ms t P3. A force F that is parallel to the x-axis acts on a block of ice. The magnitude of the force varies with the x-coordinate of the block as shown. Calculate the work done on the block of ice by the force F when the block moves from x = 0 m to x = 7.0 m. 2 1 0 1 2 3 4 5 6 7 F / N x / m

National Junior College Science Department | Physics P4. N14/P1/Q17 A long nylon fibre is stretched by a force that is increased from zero to a final value F. The force-extension graph is obtained for this process is shown below. When the force is subsequently reduced from F to zero, the force-extension graph obtained is shown below. Which combination of areas from these graphs give the net work done on the fibre? A K – L B K + L C P – Q D P + Q 4.3 KINETIC ENERGY 4.3.1 Exercises E6 Sam pushes a 10 kg sack of rice on a frictionless surface with a constant horizontal force of 2.0 N starting from rest. (a) What is the energy in the kinetic store of the sack after Sam has pushed it a distance of 35 cm? (b) What is the speed of the sack after Sam has pushed it a distance of 35 cm? [0.70 J; 0.37 m s-1]

National Junior College Science Department | Physics 4.4 CONCEPT OF A FIELD 4.5 POTENTIAL ENERGY 4.5.1 Exercises E7. A roller coaster is shown in figure below. Assuming no friction, and that the coaster has a speed of 2.80 m s-1 at point A, calculate (a) the speed at point B, and [24.4 m s-1] (b) the speed at point C. [10.3 m s-1] E8. A block of mass 2.0 kg placed on a smooth table is pressed against a spring as shown below. The spring is compressed by a distance of 10.0 cm from its unstretched length. The block is released and it accelerates until it leaves the spring at O. The spring has a spring constant of 500 N m-1. Calculate (a) the work done in compressing the spring. [2.5 J] (b) the speed of the block when it leaves O. [1.6 m s-1] 4.5.2 Problems P5. In the process of crossing an obstacle course, a 65 kg student running at 5.0 m s −1 grabs a hanging rope of length 2.0 m, and swings out over a pit of water. He releases the rope when his speed is 2.0 m s−1. What is the angle  when he releases the rope? 2.0 m 

National Junior College Science Department | Physics P6. N13/P1/Q10 Which row in the table gives the gravitational potential energy, the elastic potential energy and the kinetic energy of a bungee jumper during the first fall? Air resistance is negligible. gravitational potential energy/ kJ elastic potential energy/ kJ kinetic energy/ kJ A top middle bottom 120 60 0 0 10 120 0 50 0 B top middle bottom 120 60 0 0 30 60 0 30 60 C top middle bottom 120 60 0 0 30 120 0 60 0 D top middle bottom 120 60 0 0 60 120 0 0 0 P7. An 80.0 kg sky diver jumps out of a balloon at an altitude of 1000 m and opens the parachute at an altitude of 200 m. The total retarding force on the diver is constant at 50.0 N with the parachute closed and constant at 3600 N with the parachute open. (a) What is the speed of the diver when he lands on the ground? (b) At what height should the parachute be opened so that the final speed of the sky diver when he hits the ground is 5.00 m s-1?

National Junior College Science Department | Physics P8. 2009 H1 P2 Q7 Fig. 8.1 shows a man doing a bungee jump. Fig. 8.1 The man has a mass of 75 kg and falls a distance of 41 m before the elastic rope attached to him starts to exert a force on him. (a) (i) Calculate the theoretical time for a fall of this distance. [2] (ii) The actual time taken for the fall is 2.9 s. State the deduction you can make by comparing the actual time with your answer to (i). [1]

National Junior College Science Department | Physics (b) A force-extension graph for the elastic rope used for the bungee jump is shown in Fig. 8.2. Fig. 8.2 The total distance of fall for the man before he stops for the first time is 73 m. Deduce (i) the extension of the rope when the man stops for the first time, [1] (ii) the energy in the potential store in the rope at this time. [1]

National Junior College Science Department | Physics (c) (i) Complete Fig. 8.3 to show the gravitational potential energy and the kinetic energy of the man at the three points stated, together with the elastic potential energy stored in the rope. The gravitational potential energy at the bottom of the fall is taken to be zero. at the top after falling 41 m after falling 73 m (i.e. when stopped) gravitational potential energy /J 0 elastic potential energy /J kinetic energy /J [5] Fig. 8.3 (ii) Calculate 1. how far the man has fallen from the top when he has maximum kinetic energy, 2. the maximum kinetic energy of the man during the fall. (iii) Use your values to sketch three graphs on Fig 8.4 showing how the three different types of energy vary with distance fallen. Label each graph