A bullet is fired horizontally into a block connected to a spring (see below). The bullet is embedded into the block. (a) Find an expression for the amplitude of the resulting simple harmonic motion in terms of the variables given. (b) If the block then moves 7 cm before coming to rest, find (i) the bullet’s initial speed and (ii) the block’s speed when the block has moved 3 cm. Use: k = 200 N/m, M = 2 kg, and m = 200g.

Aprojectile is launched horizontally 10m above the ground and with an initial velocity of 15 m/s. a) determine the magnitude and direction of projectile velocity at t= 1.3s b) determine the magnitude and direction of projectile acceleration at t=1.3s

A23 kg log of wood begins from rest, 300 m up a sluice (a water track used to transport logs, think of it as an inclined plane with negligible friction) inclined at 20° to the horizontal. after it reaches the flat waterway at the bottom it collides elastically with a 100 kg block of wood initially at rest near the base of the incline. (a) how long does it take the 23 kg log to travel down the incline? (b) what is the speed of the 23 kg log at the bottom of the incline? (c) what are the velocities of both blocks of wood after the collision? (d) what is the total kinetic energy before the collision? (e) what is the kinetic energy of the 23 kg log after the collision? (f) what is the kinetic energy of the 100 kg block of wood after the collision? (g) what is the total kinetic energy after the collision? (h) compare the total initial and total final kinetic energies. is this consistent with what you would expect for elastic collisions? explain!

In a heat engine if 1000 j of heat enters the system the piston does 500 j of work, what is the final internal energy of the system if the initial energy was 2000 j? 1. write the equation 2.list out your known variables 3.plug the numbers into the equations 4.solve 5.write your solution statement that includes initial energy and final