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Chapter 7 Energy (Homework) Suggested Problems: 1. A weight-lifter lifts a 100 kg weight 30 cm at a constant speed. How much work does she do? Ans. 294 J 2. A child pushes a 4 kg block across the horizontal floor by pushing down on the block’s top at 37 ο below the horizontal. If the coefficient of friction is 0.4 and the block moves 1.5 m at a constant speed, how much work is done by (a) gravity? (b) The normal force? (c) Friction? (d) The child? Ans. (a) 0 (b) 0 (c) – 33.6 J (d) 33.6 J 3. When a 2 kg mass is hung vertically by a spring the spring stretches 15 cm. (a) How much further will the spring stretch if an additional 1 kg mass is attached to the spring? Instead of stretching the spring by putting the 1 kg mass on, what if a person stretches the spring the same amount. (b) How much work does the person do in stretching the spring? Ans. (a) 0.0747 m (b) 1.83 J 4. A 1.3 kg mass is moving horizontally. It starts with a speed of 3.5 m/s and ends with 32.5 J of kinetic energy. (a) Calculate its starting kinetic energy, (b) its final speed and (c) how much work was done on it by an external force. Ans. (a) 7.96 J (b) 7.07 m/s (c) 24.5 J 5. A 4000 lb mass falls from rest 12 ft where it strikes a stationary 500 lb post. The mass drives the post 1.5 ft into the ground before coming to rest. (a) How much work does gravity do on the mass from start to finish? (b) How much work does gravity do on the post from start to finish? (c) Calculate the force the mass exerts on the post while moving it. Ans. (a) 54000 ft-lb (b) 750 ft-lb (c) 36000 lb 6. A 10 kg mass is lifted 1.5 m straight up then moved horizontally 2.6 m. (a) Calculate the total work done by the gravitational force during these two moves. A second 10 kg mass is moved along a 30 ο incline 3 m. (b) Calculate the work done by gravity during this second move? (Note the two masses start and end at the same location.) Ans. (a) – 147 J (b) – 147 J Challenging Problems: 1. The top end of spring #1 is attached to the ceiling and it hangs vertically. Spring #2 is attached to the lower end of the first spring. The spring constant of spring #1 is 150 N/m and of spring #2 is 300 N/m. (a) If a 2.5 kg mass is attached to the lower end of spring #2, by how much does the system stretch? (b) What is the system’s effective spring constant? Ans. (a) 0.246 m (b) 99.7 N/m