A metal block is sliding down a frictionless inclined ramp that makes 35 degrees with respect to the horizontal, and it takes 4.8 seconds to reach the bottom of the ramp. Now if a sand paper is inserted between the metal block and the ramp, and the run is repeated, it takes longer time to reach the bottom of the ramp because now there is a frction between the metal block and the ramp with the coefficient of kinetic friction being μk = 0.19. Based on these experimental data, what is the velocity of the block when it reaches the bottom of the ramp for the latter frictional run? please show work

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.

What makes thermal imaging cameras useful? they can detect differences in color. they can detect differences in wave speeds. they can detect differences in temperature. they can detect mechanical waves.

6–48 bananas are to be cooled from 24 to 138c at a rate of 215 kg/h by a refrigeration system. the power input to the refrigerator is 1.4 kw. determine the rate of cooling, in kj/ min, and the cop of the refrigerator. the specific heat of banana above freezing is 3.35 kj/kg·8c.