Alead bullet at 27°c just melts when stopped by an obstacle. assuming that 25 % of heat is absorbed by the obstacle, find the velocity of the bullet if its initial temperature is 27^{\circ}c. [for lead, melting point = 327^{\circ}c, specific heat = 0.03 cal/g-^{\circ}c, latent heat of fusion = 6 cal/g and j = 4.2 j/cal.]

Three different objects, all with different masses, are initially at rest at the bottom of a set of steps. each step is of uniform height . the mass of each object is a multiple of the base mass : object 1 has mass 4..00m , object 2 has mass 1..96m , and object 3 has mass . when the objects are at the bottom of the steps, define the total gravitational potential energy of the three-object system to be zero. if the objects are then relocated as shown, what is the new total potential energy of the system? each answer requires the numerical coefficient to an algebraic expression. each algebraic expression is given using some combination of the variables , , and , where is the acceleration due to gravity. enter only the numerical coefficient. (example: if the answer is 1..23mgd , just enter 1.23)

1. jay fills a wagon with sand (about 20 kg) and pulls it with a rope 30 m along the beach. he holds the rope 25° above the horizontal. the rope exerts a 20-n tension force on the wagon. how much work does the rope do on the wagon?

What energy transformations occur each time the skateboarder rolls up the ramp?