Parker is a 56 kg pole vaulter and after successfully completing a vault, her center of mass achieves a maximum peak of height of 4.6 meters after pole-vaulting over the crossbar set at that height. She lands on a thick crash pad and when she first makes contact with the mat, her center of mass is 0.9 meters above the ground. During her impact with the mat, the mat undergoes a maximum compression at the point when her vertical velocity reaches 0 m/s and her center of mass is 0.3 meters from the ground. a) What is Parker’s maximum potential energy during the vault? b) What is Parker’s maximum kinetic energy during the landing phase of the vault? c) What is Parker’s maximum speed in m/s during the landing phase of the vault? d) What is the work done by the crash mat on Parker during the landing in Joules to allow Parker to come to a complete stop? e) What is the magnitude of the average force in Newtons exerted by the mat on Parker to allow her to come to a stop during the landing of the…

Parker is a 56 kg pole vaulter and after successfully completing a vault, her center of mass achieves a maximum peak of height of 4.6 meters after pole-vaulting over the crossbar set at that height.  She lands on a thick crash pad and when she first makes contact with the mat, her center of mass is 0.9 meters above the ground.  During her impact with the mat, the mat undergoes a maximum compression at the point when her vertical velocity reaches 0 m/s and her center of mass is 0.3 meters from the ground. d) What is the work done by the crash mat on Parker during the landing in Joules to allow Parker to come to a complete stop? e) What is the magnitude of the average force in Newtons exerted by the mat on Parker to allow her to come to a stop during the landing of the vault?

Tarzan, who has a mass of 80 kg, holds onto the end of a vine that is at a 12° angle from the vertical. He steps off his branch and, just at the bottom of his swing, he grabs onto his chimp friend Cheetah, whose mass is 40 kg. What is the maximum angle the rope reaches as Tarzan swings to the other side?

A skateboarder with his board can be modeled as a particle of mass 76.0 kg, located at his center of mass (which we will study in Chapter 9). As shown in Figure P8.49, the skateboarder starts from rest in a crouch-ing position at one lip of a half-pipe (point ). The half-pipe is one half of a cylinder of radius 6.80 m with its axis horizontal. On his descent, the skateboarder moves without friction so that his center of mass moves through one quarter of a circle of radius 630 m. (a) Find his speed at the bottom of the half-pipe (point (b) Immediately after passing point he stands up and raises his arms, lifting his center of mass from 0.500 in to 0.950 m above the concrete (point ). Next, the skateboarder glides upward with his center of mass moving in a quarter circle of radius 5.85 m. His body is horizontal when he passes point , the far lip of the half-pipe. As he passes through point , the speed of the skateboarder is 5.14 m/s. How much chemical potential energy in the body of the skateboarder was converted to mechanical energy in the skateboarderEarth system when he stood up at point ? (c) How high above point does he rise? Caution: Do not try this stunt yourself without the required skill and protective equipment. Figure P8.49

To give a pet hamster exercise, some people put the hamster in a ventilated ball andallow it roam around the house(Fig. P13.66). When a hamsteris in such a ball, it can cross atypical room in a few minutes.Estimate the total kinetic energyin the ball-hamster system. FIGURE P13.66 Problems 66 and 67

A massive tractor is rolling down a country road. In a perfectly inelastic collision, a small sports car runs into the machine from behind. (i) Which vehicle experiences a change in momentum of larger magnitude? (a) The car does. (b) The tractor does. (c) Their momentum changes are the same size. (d) It could be either vehicle. (ii) Which vehicle experiences a larger change in kinetic energy? (a) The car does. (b) The tractor does. (c) Their kinetic energy changes are the same size. (d) It could be either vehicle.

Two metersticks are connected at their ends as shown in Figure P10.18. The center of mass of each individual meterstick is at its midpoint, and the mass of each meterstick is m. a. Where is the center of mass of the two-stick system as depicted in the figure, with the origin located at the intersection of the sticks? b. Can the two-stick system be balanced on the end of your finger so that it remains lying flat in front of you in the orientation shown? Why or why not? FIGURE P10.18 (a) The center of mass of the stick on the x axis would be at (0.5 m, 0), and the center of mass of the stick on the stick on the y axis be at (0, 0.5 m), assuming the sticks are uniform. We can then use Equation 10.3 to find the x and y coordinates of the center of mass. xCM=1Mj=1nmjxj=12m[m(0.50m)]=0.25myCM=1Mj=1nmjyj=12m[m(0.50m)]=0.25m The location of the center of mass is (0.25m,0.25m) (b) No. The location of the center of mass is not located on the object, so your finger would not be in contact with the object. In a different orientation, balancing by applying a force at the center of mass might be possible, but not in the orientation shown.

A block of mass m1 = 20.0 kg is connected to a block of mass m2 = 30.0 kg by a massless string that passes over a light, frictionless pulley. The 30.0-kg block is connected to a spring that has negligible mass and a force constant of k = 250 N/m as shown in Figure P7.73. The spring is un-stretched when the system is as shown in the figure, and the incline is frictionless. The 20.0-kg block is pulled a distance h = 20.0 cm down the incline of angle = 40.0 (so that the 30.0-kg block is 40.0 cm above the floor) and released from rest. Find the speed of each block when the 30.0-kg block is 20.0 cm above the floor (that is, when the spring is unstretched). Figure P7.73

Describe a system for which momentum is conserved but mechanical energy is not. Now the reverse: Describe a system for which kinetic energy is conserved but momentum is not.