Aday has 86,400 second (s). notice that the decimal point is to the far right of the number. the first part of scientific notation is a number between 1 and 10. move the decimal point to the left to obtain 8.64, which equals m in our traditional notation. the value for n is given by the number of places the decimal point was moved from its location in 86,400 to 8.64. thus, 86,400 s = 8.64×104 s. because the decimal was moved four places to the left (and the value is larger than 1), the exponent is a positive integer. if you had a very precise clock, you could write this as 8.640×104 s, or 8.6400×104 s. the number of digits you keep in the first part of the notation describes the precision of your value and determines the number of significant digits.

Janelle made a hypothesis bout the uneven temperatures inside her house during winter. she believes that 50% of the ducts are blocked and she plans to investigate. if she wants to prove her hypothesis using scientific processes what should she do next?

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!

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.