A 5.00 x 103 kg subway train is brought to a stop from a speed of 0.500 m/s in 0.900 m by a large spring bumper at the end of its track. What is the force constant k of the spring (in N/m)? (Enter a number.) N/m + A 2.0 kg mass starts from rest at point A and moves along the x-axis subject to the potential energy shown in the figure below. PE 30 J E 25 J 20 J 15 J 10 J S J 2m 4m 6m 8m 10m (a) Determine the speed (in m/s) of the mass at points B, C, D. (For each answer, enter a number.) point B m/s point C m/'s point D m/s (b) Determine the turning points for the mass. (Select all that apply. ) point A point B point C point D point EYou have a light spring which obeys Hooke's law. This spring stretches 2.86 cm vertically when a 2.70 kg object is suspended from it. Determine the following. (a) the force constant of the spring (in N/m) | N/m (b) the distance (in cm) the spring stretches if you replace the 2.70 kg object with a 1.35 kg object cm (c) the amount of work (in ]) an external agent must do to stretch the spring 6.50 cm from its unstretched position (a) How high (in m) a hill can a car coast up (engine disengaged) if friction is negligible and its initial speed is 82.0 km/h? (Enter a number.) m (b) If, in actuality, a 750 kg car with an initial speed of 82.0 km/h is observed to coast up a hill to a height 12.0 m above its starting point, how much thermal energy (in ]) was generated by friction? (Enter a number.) J (c) What is the average force of friction (down the slope) if the hill has a slope 2.50 above the horizontal? (Enter your answer in N. Enter a number.) N A 71.6-kg boy is surfing and catches a wave which gives him an initial speed of 1.60 m/s. He then drops through a height of 1.55 m, and ends with a speed of 8.51 m/s. How much nonconservative work (in kJ) was done on the boy? KJA man on a motorcycle plans to make a jump as shown in the figure. If he leaves the ramp with a speed of 32.0 m/s and has a speed of 30.3 m/s at the top of his trajectory, determine his maximum height (h) (in m) above the end of the ramp. Ignore friction and air resistance. m A. 5.26 kg object falls freely (ignore air resistance), after being dropped from rest. Determine the initial kinetic energy (in ]), the final kinetic energy (in ]), and the change in kinetic energy (in ]) for the following. (a) the first meter of the fall initial kinetic energy final kinetic energy change in kinetic energy (b) the second meter of the fall initial kinetic energy final kinetic energy change in kinetic energy Submit Answer(a) Find the useful power output (in W) of an elevator motor that lifts a 2400 kg load a height of 25.0 m in 12.0 s, if it also increases the speed from rest to 4.00 m/s. Note that the total mass of the counterbalanced raised in height, but the full 10,000 kg is accelerated. (Enter a number.) W (b) What does it cost (in cents), if electricity is $0.0900 per kW . h? (Enter a number.) cents (a) What is the efficiency of an out-of-condition professor who does 2.20 x 10J of useful work while metabolizing 510 kcal of food energy? (Enter your answer as a percentage. Enter a number.) 96 (b) How many food calories (in kcal) would a well-conditioned athlete metabolize in doing the same work with an efficiency of 2096? (Enter a number.) kcal (a) Calculate the force (in N) the woman in the figure below exerts to do a push-up at constant speed, taking all data to be known to three digits. (You may need to use torque methods from a later chapter.) m = 47 kg CG W 0.86 m Freaction 1.43 m (b) How much work (in ]) does she do if her center of mass rises 0.280 m? (c) What is her useful power output (in W) if she does 27 push-ups in 1 min? (Should work done lowering her body be included? See the discussion of useful work in Work, Energy, and Power in Humans.) W