Problem 6.13 The point of this question is to compare rest energy and kinetic energy at high speeds. An alpha particle (a helium nucleus) is moving at a speed of 0.9998 times the speed of light. Its mass is 6.40 × 10-27 kg. (a) What is its rest energy?

During spring semester at mit, residents of the parallel buildings of the east campus dorms battle one another with large catapults that are made with surgical hose mounted on a window frame. a balloon filled with dyed water is placed in a pouch attached to the hose, which is then stretched through the width of the room. assume that the stretching of the hose obeys hooke's law with a spring constant of 89.0 n/m. if the hose is stretched by 5.80 m and then released, how much work does the force from the hose do on the balloon in the pouch by the time the hose reaches its relaxed length? unitst 3 number-1497 the tolerance is +/-5% open show work click if you would like to show work for this question:

An engine undergoes a cycle as shown in the diagram. during a complete cycle the work done by the gas is 28.5×103 j and the energy transferred thermally out is 99.4×103 j. there are 1.5×1024 gas molecules and they have three active degrees of freedom. 6. (6 pts) during which process(es) is energy transferred thermally into the gas? a. 1→2 b. 2→3 c. 4→1 d. 1→2 and 4→1 e. none of the above

Aleaky 10-kg bucket is lifted from the ground to a height of 15 m at a constant speed with a rope that weighs 0.7 kg/m. initially the bucket contains 45 kg of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 15-m level. find the work done. (use 9.8 m/s2 for g.) show how to approximate the required work by a riemann sum. (let x be the height in meters above the ground. enter xi* as xi.) lim n → ∞ n (9.8)(45−3 xi) i = 1 δx express the work as an integral. 0 dx evaluate the integral. (round your answer to the nearest integer.) j