Usain Bolt's world-record 100 m sprint on August 16, 2009, has been analyzed in detail. At the start of the race, the 94.0 kg Bolt accelerated from rest at a rate of 9.50 m/s for the first 0.890 s, and eventually reached a top speed of 12.4 m/s by exerting an average horizontal force of 820 N against the ground for the entire 9.58 s duration of the race. (a) What was the average horizontal force (in N) exerted by Bolt against the ground during the first 0.890 s of the race? 893 N (b) What was Bolt's speed (in m/s) after the initial acceleration phase? 8.5 m/s (c) What was the power expended by Bolt during the initial acceleration phase? (Give the magnitude of your answer in W.) 3816 w (d) It has been shown that, because of his large frame and 6'5" height, Bolt experienced significant drag forces during the sprint. To estimate the energy lost to drag forces during the race, let's focus on the remaining 9.58 s - 0.890 s = 8.69 s of the race after Bolt's initial burst of acceleration. The drag force varies with speed, but let's find an average drag force over the last 8.69 s of the race. Model the drag force as a friction force and find the increase in internal energy of Bolt and the surrounding air in these 8.69 s as Bolt runs through the air. (Give your answer in J.) 812.5 X Consider the force exerted by Bolt. Is this force only opposing the drag force on the runner? What is the net force during the second part of the race and how does this relate to the change in internal energy of the system? J (e) Finally, find the power that Bolt must expend just to overcome the drag force and compare it to the result in part (c). (Give the magnitude of your answer in W.) 8030 X How are energy and power related? During what time interval is the power to overcome air resistance expended? WA 1.10-kg object slides to the right on a surface having a coefficient of kinetic friction 0.250 (Figure a). The object has a speed of v; = 3.10 m/s when it makes contact with a light spring (Figure b) that has a force constant of 50.0 N/m. The object comes to rest after the spring has been compressed a distance d (Figure c). The object is then forced toward the left by the spring (Figure d) and continues to move in that direction beyond the spring's unstretched position. Finally, the object comes to rest a distance D to the left of the unstretched spring (Figure e). a m vi b d C V.= 0 d O = A e (a) Find the distance of compression d (in m). m (b) Find the speed v (in m/s) at the unstretched position when the object is moving to the left (Figure d). m/s (c) Find the distance D (in m) where the object comes to rest. m (d) What If? If the object becomes attached securely to the end of the spring when it makes contact, what is the new value of the distance D (in m) at which the object will come to rest after moving to the left? mAs shown in the figure below, a light string that does not stretch changes from horizontal to vertical as it passes over the edge of a table. The string connects me, a 3.30 kg block, originally at rest on the horizontal table at a height 1.30 m above the floor, to m,, a hanging 2 kg block originally a distance d = 0.990 m above the floor. Neither the surface of the table nor its edge exerts a force of kinetic friction. The blocks start to move from rest. The sliding block m, is projected horizontally after reaching the edge of the table. The hanging block m, stops without bouncing when it strikes the floor. Consider the two blocks plus the Earth as the system. mo (a) Find the speed at which m, leaves the edge of the table. (Assume m, hits the ground before m, leaves the table.) 4.4 X Your response differs from the correct answer by more than 10%. Double check your calculations. m/s (b) Find the impact speed of m, on the floor. 6.7 X Your response differs from the correct answer by more than 10%. Double check your calculations. m/s (c) What is the shortest length of the string so that it does not go taut while m, is in flight? 2.26 X Your response differs from the correct answer by more than 10%. Double check your calculations. m (d) Is the energy of the system when it is released from rest equal to the energy of the system just before m, strikes the ground? O Yes O No (e) Why or why not? yes, conservation forceShown below is a waterslide constructed in the late 1800's. This slide was unique for its time due to the fact that a large number of small wheels along its length made friction negligible. Riders rode a small sled down the chute which ended with a horizontal section that caused the sled and rider to skim across the water much like a flat pebble. The chute was 9.76 m high at the top and 54.3 m long. Consider a rider and sled with a combined mass of 72.5 kg. They are pushed off the top of the slide from point A with a speed of 2.85 m/s, and they skim horizontally across the water a distance of 50 m before coming to rest. Engraving from Scientific American July 1888 (a 20.0 m A B 9.76 m C -54.3 m- -50.0 m (b) (a) Find the speed (in m/s) of the sled and rider at point C. m/s (b) Model the force of water friction as a constant retarding force acting on a particle. Find the magnitude (in N) of the friction force the water exerts on the sled. N (c) Find the magnitude (in N) of the force the chute exerts on the sled at point B. N (d) At point C the chute is horizontal but curving in the vertical plane. Assume its radius of curvature is 20.0 m. Find the force (in N) the chute exerts on the sled at point C. magnitude direction ---Select--- v