Classical Mechanics Answers

Let the force of gravity to be constant for small distances above the surface of the earth. A body is dropped from rest at a height h above the earth surface. What will be its kinetic energy just before it strikes the ground?

Four point masses of mass each of 1 kg are connected by a string which forms a square of diagonal 0.707 m . If square is placed on rotating table rotating with 5 rotation per second then what is the tension in string ?

Four persons A,B,C,D travel along a square of side d such that each one face the other after how much time they meet ?

A particle of mass m is attached to the end of a string and moves in a circle of radius of radius r on a frictionless horizontal table. The string passes through a frictionless hole in the table and, initially, the other end id fixed. a) if the string is pulled so that the radius of the circular orbit decreases, how does the angular velocity change if it is ω0 when r = r0? b) what work is done when the particle is pulled slowly in from a radius r0 to a radius r0/2? 

A particle of mass m is attached to the end of a string and moves in a circle of radius of r on a frictionless horizontal table. The string passes through a frictionless hole in the table and, initially, the other end id fixed.

a) if the string is pulled so that the radius of the circular orbit decreases, how does the angular velocity change if it is ω₀ when r = r₀?

b) what work is done when the particle is pulled slowly in from a radius r₀ to a radius r₀/2?

A force f̂ is expressed with respect to the basis ê₁ and ê₂ by equation 2(3 ê₁ +4 ê₂) N. If the directions of ê₁ makes an angle of 30 degree with f̂, find the vector ê₂.

Let the force of gravity be constant for small distances above the surface of the earth. A body is dropped from rest at a height h above the earth surface. What will be its kinetic energy just before it strikes the ground?

Explain dimension of phase space

An object of mass m and initial position ⃗r₀ and initial velocity ⃗v₀ is moving under the action of the gravitational force near to earth surface at some latitude λ. Neglect the effects of both the air resistance and wind.

a) Choose your latitude and describe your system in detail.

b) Name all the forces acting on the object and sketch the free-body diagram (FBD) due to the dominant forces only.

c) Write the equation of motion (EOM) for the object and its general solutions.

d) Use relevant octave script to plot the position (trajectory) of the object when it is released from initial height z’₀ = h₀ and describe the motion.

e) Use the same script to plot the position of the object when it is launched with initial velocity ⃗v₀ at initial position ⃗r₀ and describe the motion.