Classical Mechanics Answers

A piece of ice of mass mice = 80g, which is initially at -15℃ is dropped into an isolated container with negligible heat capacity. The container contains 150g of water at 80℃. Determine the final temperature of the system? 

(Ci = 2093 J/kg℃, Cw = 4186 J/kg℃, Lf = 333 KJ/kg)

For an elliptical orbit in gravity with energy E and angular momentum L, (a) find an expression for the semi-major axis (in terms of m, M, G, E, and L) and (b) for the eccentricity. This is also how the book operates: in our language, the equation for u = 1/r is 

For numbers 3 & 4, it is easier to use the differential equation for the orbit that comes from analysis of the FORCES, not the ENERGETICS. This is also how the book operates: in our language, the equation for u = 1/r is  [The book’s equation contains the parameter ℓ which is just L/m, a constant; NOT the latus rectum, but related to it since both depend on for the inverse-square force. The orbits in 3 & 4 have no definable latus rectum].

the flow in a lake is 0.5 m ^ 3 / s. a water fall in the lake has a height of 1.5m. with a thermal efficiency of 40%, how much power can be added

A block of mass m1 = 20.0 kg is connected to a block of mass m2 = 30.0 kg by a massless string that passes over a light, frictionless pulley. The 30.0-kg block is connected to a spring that has negligible mass and a force constant of k = 250 N/m.The spring is unstretched when the system is as shown in the figure, and the incline has a coefficient of friction of 0.2. The 20.0-kg block is pulled a distance d = 20.0 cm down the incline of angle of 30.0 degrees and released from rest. Find the speed of each block when the spring is again unstretched.

Find the moment of inertia and the radius of gyration for 2x + 3y = 6, x = 0, y = 0; about the x - axis

Find the moment of inertia and the radius of gyration for bx + ay = ab, x = 0, y = 0, about the y - axis

1. A load roller with a weight of 15 N lifts a load of 18 kg. The free end of the rope is subjected to a force of 105 N. Calculate the friction force.
2. The length of one inclined plane is 6 m, the other - 7.2 m. In the first plane the body is raised to a height of 1.5 m, and in the second - to 1.8 m. Which of these planes can win more power?

A cylindrical tank of radius 3 ft and height 10 ft stands on a flatform 50 ft high. How much work will be done in filling the tank by pumping water from the ground level?

If a force of 5 lb produces a stretch of one-tenth the natural length L ft of a spring. How much work will be done in stretching the spring to double its natural length?

An upstretched spring is 10 ft. long. A pull of 40 lb stretches the spring by 1/2 ft. Find the work done in stretching from 10 ft. to 14 ft.