The crate of mass m = 41 kg is attached to the springs with constants k1 = 1 kN/m and k2 = 2 kN/m. Both springs are unstretched when δ = 0 and the box is centered between the two vertical walls. The crate is released from rest after being displaced a distance δ = 2 m and the coefficient of kinetic friction between the crate and the surface on which it slides is μk = 0.2.

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.

An object has a weight of 500 on earth what is the mass of this object

Classify each possible hypothesis about a medicinal aloe vera plant as falsifiable or non-falsifiable. aloe vera gel is the best natural skin moisturizer. aloe vera gel can heal wounds by boosting cell renewal. aloe vera juice tastes better than carrot juice. drinking aloe juice can reduce the risk of lung cancer.