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Classical Mechanics
Equation of motion of free falling object using lagrangian mechanics
Classical Mechanics
The magnitude of Coriolis accelaration for a particle of mass m moving with a velocity 100m/s horizontally along eath's surface at the north pole is about?
Classical Mechanics
The type of constraints on the mechanical system consisting of a cyllinder rolling (and possibilly sliding) down an inclined plane of angle alpha are? (please try to explain the reasons also)
Classical Mechanics
Determine the amount of kinetic energy absorbed by the brakes when a car is travelling at 60km/hr and brakes to 40km/hr?
Classical Mechanics
A car starts from rest and attains the velocity of 60km/h in 5 minutes. It travels at the constant velocity for 1 minute and then decreases its speed to 30 km/h in another 5 minutes. Calculate the acceleration in si units in both the cases.
Classical Mechanics
Consider a pendulum of mass “m” attached to a spring of mass “M” that is free to move in
single dimension along a frictionless horizontal surface. Take the gravity g = 10 m/s2
and the
gravitational potential energy is equal to zero at the level of block (y = 0).
a) Write the equations of constraints.
b) Determine the degree of freedom (S = ??)
c) Write the expression of r⃗⃗⃗M⃗ as a function of X and unit vector i
d) Write the expression of r′m
⃗⃗⃗⃗⃗⃗ as a function of unit vector i , e′r
⃗⃗⃗⃗⃗ and e′θ
⃗⃗⃗⃗⃗
e) Find the expression of kinetic energy of the system as a function of (M, m, Ẋ
, l, θ, θ̇)
f) Write the expression of potential energy PE of the system as a function of (m, l, θ)
g) Write the Lagrangian equation
h) Deduce the equations of motion from Euler-Lagrange equations
single dimension along a frictionless horizontal surface. Take the gravity g = 10 m/s2
and the
gravitational potential energy is equal to zero at the level of block (y = 0).
a) Write the equations of constraints.
b) Determine the degree of freedom (S = ??)
c) Write the expression of r⃗⃗⃗M⃗ as a function of X and unit vector i
d) Write the expression of r′m
⃗⃗⃗⃗⃗⃗ as a function of unit vector i , e′r
⃗⃗⃗⃗⃗ and e′θ
⃗⃗⃗⃗⃗
e) Find the expression of kinetic energy of the system as a function of (M, m, Ẋ
, l, θ, θ̇)
f) Write the expression of potential energy PE of the system as a function of (m, l, θ)
g) Write the Lagrangian equation
h) Deduce the equations of motion from Euler-Lagrange equations
Classical Mechanics
A motorist drives south at 20 m/s for 3 min, then turns west and travels at 25 m/s for 2 min, and finally travels northwest at 30 m/s for 1 min. For this 6 min trip find the average velocity.
Classical Mechanics
A puck of mass 80.0 g and radius 4.00 cm slides along an
air table at a speed of 1.50 m/s. It makes a glancing collision with a second puck
of radius 6.00 cm and mass 120 g (initially at rest) such
that their rims just touch. Because their rims are coated
with instant-acting glue, the pucks stick together and spin
after the collision (Fig. P11.34b). (a) What is the angular
momentum of the system relative to the center of mass?
(b) What is the angular speed about the center of mass?
air table at a speed of 1.50 m/s. It makes a glancing collision with a second puck
of radius 6.00 cm and mass 120 g (initially at rest) such
that their rims just touch. Because their rims are coated
with instant-acting glue, the pucks stick together and spin
after the collision (Fig. P11.34b). (a) What is the angular
momentum of the system relative to the center of mass?
(b) What is the angular speed about the center of mass?
Classical Mechanics
A particle starts from the origin with velocity 5
Classical Mechanics
In the system shown, a horizontal force Fx = 40 N acts on an object of mass m2 = 8.00 kg. A friction force fk = 5 N acts between object m2 and the table top, and m1 = 2.00 kg. i) Calculate the acceleration of the masses. ii) Calculate the tension in the string.
