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- A child of mass m starts from rest and slides without friction from a height h along a slide next to a pool (Fig. P7.27). She is launched from a height h/5 into the air over the pool. We wish to find the maximum height she reaches above the water in her projectile motion. (a) Is the childEarth system isolated or nonisolated? Why? (b) Is there a nonconservative force acting within the system? (c) Define the configuration of the system when the child is at the water level as having zero gravitational potential energy. Express the total energy of the system when the child is at the top of the waterslide. (d) Express the total energy of the system when the child is at the launching point. (e) Express the total energy of the system when the child is at the highest point in her projectile motion. (f) From parts (c) and (d), determine her initial speed vi at the launch point in terms of g and h. (g) From parts (d), (e), and (f), determine her maximum airborne height ymax in terms of h and the launch angle . (h) Would your answers be the same if the waterslide were not frictionless? Explain. Figure P7.27(a) Calculate the force needed to bring a 950-kg car to rest from a speed of 90.0 km/h in a distance of 120 m (a fairly typical distance for a non-panic stop). (b) Suppose instead the car hits a concrete abutment at full speed and is brought to a stop in 2.00 m. Calculate the force exerted on the car and compare it with the force found in part (a).You have a new internship, where you are helping to design a new freight yard for the train station in your city. There will be a number of dead-end sidings where single cars can be stored until they are needed. To keep the cars from running off the tracks at the end of the siding, you have designed a combination of two coiled springs as illustrated in Figure P7.41. When a car moves to the right in the figure and strikes the springs, they exert a force to the left on the car to slow it down. Both springs are described by Hookes law and have spring constants k1 = 1 600 N/m and k2 = 3 400 N/m. After the first spring compresses by a distance of d = 30.0 cm, the second spring acts with the first to increase the force to the left on the car in Figure P7.41. When the spring with spring constant k2 compresses by 50.0 cm, the coils of both springs are pressed together, so that the springs can no longer compress. A typical car on the siding has a mass of 6 000 kg. When you present your design to your supervisor, he asks you for the maximum speed that a car can have and be stopped by your device. Figure P7.41
- Suppose a 350-g kookaburra (a large kingfisher bird) picks up a 75-g snake and raises it 2.5 m from the ground to a branch. (a) How much work did the bird do on the snake? (b) How much work did it do to raise its own center of mass to the branch?(a) Calculate the force needed to bring a 950-kg car to rest from a speed of 90.0 km/h in a distance of 120 m (a fairly typical distance for a non-panic stop). (b) Suppose instead the car hits a concrete abutment at full speed and is brought to a stop in 2.00 m. Calculate the force exerted on the car and compare it with the force found in part (a).Two particles of masses m1 and m2 separated by a horizontal distance D are let go from the same height h at different times. Particle 1 starts at t=0 , and particle 2 is let go at t=T . Find the vertical position of the center of mass at a time before the first particle strikes the ground. Assume no air resistance.
- A small 0.65-kg box is launched from rest by a horizontal spring as shown in Figure P9.50. The block slides on a track down a hill and comes to rest at a distance d from the base of the hill. Kinetic friction between the box and the track is negligible on the hill, but the coefficient of kinetic friction between the box and the horizontal parts of track is 0.35. The spring has a spring constant of 34.5 N/m, and is compressed 30.0 cm with the box attached. The block remains on the track at all times. a. What would you include in the system? Explain your choice. b. Calculate d.A box is being moved to the right at a constant velocity v by a force P (parallel to v) along a level horizontal floor. The normal force is FN, the kinetic frictional force is fk , and the weight of the box is mg. (a) Draw a free-body diagram of this situation. (b) Decide which forces do positive, zero and negative work. Give your reasoning.86 Please use energy to solve Please label all free body diagrams and any formulas used Thanks!
- 7. The problem is all about Thevenin, Norton, and Millman's Theorems, and Maximum Power Transfer. Please PROVIDE FREE BODY DIAGRAM. And please PROVIDE MATRIX FORM in the solution.Answer the question and explain why you pick the answer. The gravitational potential energy of a two-object system ____________? a) Decreases in magnitude if the objects become more massive b) Can be positive or negative c) None of the aboveTwo flat stone blocks of masses 100kg each are stacked on top of one another on the back of a truck. The coefficient of static friction between the bottom block and the truck is 0.8 and between the two blocks is 0.7. (Describe how you get the answers per question!) a) What is the maximum acceleration the truck can have such that neither of the blocks slide off ? b) If the truck accelerates from rest at this maximum acceleration for 6 seconds, how much more energy will the truck's engine need to output compared to if the stone blo cks were not on the truck? c) What is the maximum speed that the truck can drive around a curve of minimum curvature radius 100m without either of the blocks sliding off ? d) What is the maximum slope that the truck can drive up at constant speed without either of the blocks sliding off?