Classical Mechanics Answers

Calculate the minimum velocity with which water of coefficient of viscosity 0.001Nsm^-2 flows through a tube of radius 6×10^-4 m, without turbulence being produced.Reynolds number is 1000. Find the rate of flow of water through the tube at this velocity and the pressure is required to maintain it if the length of the tube is 0.2m

A pendulum of mass m and length b is attached to a massless support initially at rest and then moving with vertically upward acceleration a

( a) Determine the Lagrangian

( b) Find the equation of motion of the pendulum

Refer to the figure below

A 400 kg mass on 30∘ inclined plane is acted upon by a force equal to 4800 N at an angle 30∘ with the incline as shown in the figure below.

a) Find the acceleration of the mass if the incline is frictionless

b) Find the acceleration of the mass if the coefficient of fiction between the mass and inclined plane is μk=0.2 

For the system of two blocks on a frictionless double incline where the blocks are linked by an inextensible massless string over a frictionless pulley (see figure),

(a). Draw the free body diagram for m₁ and m₂.

(b). Express the equations of motion of the two blocks using Newton's Laws

(c). Prove that for the system to be in equilibrium

The bob of the pendulum is 200 g. It is swinging at a height of 1 m. The length of the pendulum is 1 m. Find the values of GPE, KE, and total mechanical energy at a height of 1 m, 0.5 m and 0.25 m and at its lowest point.

An airplane has a mass of 35,000 kg and a take off acceleration of 1.20 m/s^2 in 20 m. How much work was done by the take off of the airplane? What is the power if the work was done in 10 seconds?

Two smooth spheres of weight 100N and radius of 250mm each are in equilibrium in a

horizontal channel of width 870mm as shown in the figure 1. Find the reactions at the contact

surfaces A, B, C and D, assuming all surfaces to be frictionless.

a particle is moving along a straight line with the acceleration a= (15 t− 7t^2/3) ft/s^2, where t? is in seconds. determine the velocity and the position of the particle as a function of time when t= 0, v= 0 and x= 15 ft.

The position of a point is given as a function of time by x= 4t − 6t + 2t− 1 , where x and t are expressed in meters and seconds. Determine the position, the velocity, and the acceleration of the particle when t= 2 s.

The acceleration of a point is a= 20t m/s2. When t= 0, x= 40 m and v= - 10 m/s. What are the position and velocity at t= 3 s?