Example 3 in einstein's theory of special relativity the mass of an object moving with velocity v is m = m0 1 − v2/c2 where m0 is the mass of the object when at rest and c is the speed of light. the kinetic energy of the object is the difference between its total energy and its energy at rest: k = mc2 − m0c2. (a) show that when v is very small compared with c, this expression for k agrees with classical newtonian physics: k = 1 2 m0v2. (b) use taylor's inequality to estimate the difference in these expressions for k when |v| ≤ 50 m/s.

John throws .4 kg ball with velocity of 18 m/s. hits .2 kg bottle and bottle flies 25 m/s. how fast is ball traveling after hitting the bottle?

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)

The diagram shows a series of volcanic island and a hot spot determine the direction of movement of the tectonic plate that for the island