NJC 2023 Work, Energy, Power Problem Set

National JC Work, Energy and Power 2023 - 1 - WEP Problem Set Exercises Work done E1. (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] E2. (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. Force-extension, EPE E3. The elastic potential energy stored in the bow just before the release of an arrow is 95 J. When the arrow of mass 170 g is fired, 90% of the elastic potential energy is transferred to the arrow. Show that the speed of the arrow as it leaves the bow is 32 m s-1. E4. An object at rest is pulled by a constant horizontal force, F on a smooth floor to a displacement of x. (i) Sketch a graph of force applied on object against the displacement. Label F and x in the graph. (ii) What does the area under force against displacement graph in (i) represent? Hint: work done. E5. An object at rest is pulled by a varying horizontal force, Fx on a smooth floor to a displacement of x. (i) Can we still use this formula to calculate the work done by Fx, i.e workdone = Fx(x)? (ii) How can the work done by Fx be calculated? Kinetic energy 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 kinetic energy 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] Conservation of Energy 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]

National JC Work, Energy and Power 2023 - 2 - 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] Power E9. 2009/P1/Q12 A speed boat with two engines, each of power output 36 kW, can travel at a maximum speed of 12 m s-1. The total drag D on the boat is related to the speed v of the boat by the equation shown. 2 vD  What is the maximum speed of the boat when only one engine is working? [D] A 3.0 m s-1 B 6.0 m s-1 C 8.5 m s-1 D 9.5 m s-1 Problems Work P1. 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. [C] Which value of kinetic energy is given to the object? A Fst B Fv C Fs D 2 ms t P2. 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. [3.0 J] 2 1 0 -1 1 2 3 4 5 6 7 F / N x / m

National JC Work, Energy and Power 2023 - 3 - Work done: Force-extension graph P3. N14/P1/Q17, TYS: Topic 4: MCQ 3 [C] Conservation of energy P4. 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? 62o 2.0 m 

National JC Work, Energy and Power 2023 - 4 - P5. 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 [B] P6. N13/P1/Q10, TYS: Topic 5: MCQ 2 [A] 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? [24.9 m s-1] (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? [207 m]

National JC Work, Energy and Power 2023 - 5 - 8. 2009 H1 P2 Q7 2.89 s

National JC Work, Energy and Power 2023 - 6 - 32 m 5.4 x 104 J

National JC Work, Energy and Power 2023 - 7 - [48 m, 3.3 x 104 J]

National JC Work, Energy and Power 2023 - 8 - Power P9. A car of mass 1200 kg starts from rest at the foot of a hill inclined at an angle  to the horizontal, where sin  = 1/5. 3.0 minutes later, the car has a speed of 20.0 m s -1 and has travelled a distance of 1.6 km. The frictional forces resisting the motio n are constant and of magnitude 210 N. Calculate, in this time, the average power of the engine of the car. [2.41x104 W] P10. N15/1/8, TYS Topic 5: MCQ 5 [C] P11.A tugboat, moving by itself in calm water, requires 80 kW at the propeller to move with a steady speed of 5.0 m s-1. When towing a large ship at the same steady speed, 600 kW must be delivered to the propeller. Calculate the force in the towline. [ 1.04 x 105 N] P12. N12/P1/19 [B] Efficiency P13. N16/P1/11, TYS Topic 5: MCQ 7 [A]

National JC Work, Energy and Power 2023 - 9 - P14. N13/P1/11, TYS Topic 5: MCQ 1 [C]