A skateboarder with his board can be modeled as a particle of mass 80.0 kg, located at his center of mass. As shown in the figure below, the skateboarder starts from rest in a crouching position at one lip of a half-pipe (point). On his descent, the skateboarder moves without friction so that his center of mass moves through one quarter of a circle of radius 6.20 m. i (a) Find his speed at the bottom of the half-pipe (point Ⓡ). m/s (b) Immediately after passing point Ⓑ, he stands up and raises his arms, lifting his center of mass and essentially "pumping" energy into the system. Next, the skateboarder glides upward with his center of mass moving in a quarter circle of radius 5.71 m, reaching point D. As he passes through point ①, the speed of the skateboarder is 5.37 m/s. How much chemical potential energy in the body of the skateboarder was converted to mechanical energy when he stood up at point Ⓑ? ] (c) How high above point ① does he rise? m

A 31.0-kg child on a 3.00-m-long swing is released from rest when the ropes of the swing make an angle of 29.0° with the vertical. (a) Neglecting friction, find the child's speed at the lowest position. m/s (b) If the actual speed of the child at the lowest position is 2.40 m/s, what is the mechanical energy lost due to friction? ]

A force acting on a particle moving in the xy plane is given by F = (2yî + x²), where F is in newtons and x and y are in meters. The particle moves from the origin to a final position having coordinates x = 5.60 m and y = 5.60 m, as shown in the figure below. y (m) B (x, y) x (m) (a) Calculate the work done by F on the particle as it moves along the purple path (0 Ⓐ©). ] (b) Calculate the work done by ♬ on the particle as it moves along the red path (0 BC). J (c) Is F conservative or nonconservative? ○ conservative nonconservative