1. Calculate the work done by a 47 N force pushing a pencil 0.26 m. Work is calculated by the formula $$W = F \times d$$ where $F$ is the force and $d$ is the displacement. $$W = 47 \times 0.26 = 12.22\,\text{J}$$ 2. Calculate the work done by a 47 N force pushing a 0.025 kg pencil 0.25 m against a force of 23 N. The net force doing work is $47 - 23 = 24\,N$. $$W = 24 \times 0.25 = 6.0\,\text{J}$$ 3. Calculate the work done by a 2.4 N force pushing a 400 g sandwich 0.75 m wide. Convert 400 g to kg: $0.400$ kg, but mass is not directly needed here. $$W = 2.4 \times 0.75 = 1.8\,\text{J}$$ 4. How far can a mother push a 20.0 kg baby carriage using 62.0 N force if she can do 2920 J of work? $$d = \frac{W}{F} = \frac{2920}{62.0} = 47.1\,\text{m}$$ 5. How much work is it to lift a 20. kg sack of potatoes vertically 6.5 m? Calculate force as weight: $F = mg = 20 \times 9.8 = 196\,N$ $$W = F \times d = 196 \times 6.5 = 1274\,\text{J}$$ 6. If a small motor does 520 J of work to move a toy car 260 m, what force does it exert? $$F = \frac{W}{d} = \frac{520}{260} = 2.0\,N$$ 7. A girl pushes her brother on a sled with 300 N for 750 m. (a) Net force = $300 - 200 = 100 N$ $$W = 100 \times 750 = 75000\,\text{J}$$ (b) Net force = $300 - 300 = 0 N$ $$W = 0 \times 750 = 0\,\text{J}$$ 8. A 75.0 kg man pushes a 5.0 x 10^5 kg wall for 250 s but it does not move. No displacement means no work. $$W = 0\,\text{J}$$ 9. A boy drags a wagon at 0.800 m/s for 30.0 min with 40.0 N force. Convert time to seconds: $30.0 \times 60 = 1800$ s. Distance $d = v \times t = 0.800 \times 1800 = 1440\,m$ $$W = 40.0 \times 1440 = 57600\,\text{J}$$ 10. If it takes 25 N to slide the box up the ramp, work depends on distance which is not given. Cannot solve without distance. 11. How much power does it take to lift 30.0 N 10.0 m high in 5.00 s? Work: $W = 30.0 \times 10.0 = 300\,J$ Power: $P = \frac{W}{t} = \frac{300}{5.00} = 60.0\,W$ 13. How much power to lift 30.0 kg 10.0 m high in 5.00 s? Force: $F = mg = 30.0 \times 9.8 = 294\,N$ Work: $W = 294 \times 10.0 = 2940\,J$ Power: $P = \frac{2940}{5.00} = 588\,W$ 14. You move a 25 N object 5.0 meters. Work: $$W = 25 \times 5.0 = 125\,J$$ 15. You carry a 20. N bag of dog food up 6.0 m stairs. $$W = 20 \times 6.0 = 120\,J$$ 16. You push down on a 3.0 N box for 10 minutes. Work involves displacement; assuming no displacement downward (not given), work = 0 J. 17. You use 35 J of energy to move a 7.0 N object. How far? $$d = \frac{W}{F} = \frac{35}{7.0} = 5.0\,m$$ 18. You do 45 J of work in 3.0 seconds. Power: $$P = \frac{45}{3.0} = 15.0\,W$$ 19. A car uses 2500 J in 25 seconds. Power: $$P = \frac{2500}{25} = 100\,W$$ 20. A 60-watt bulb runs 5.0 seconds. Energy used: $$E = P \times t = 60 \times 5.0 = 300\,J$$ 21. How much work can a 22-kW car engine do in 60s at 100% efficiency? $$W = P \times t = 22000 \times 60 = 1320000\,J$$