Classical Mechanics Answers

A particle of mass m is projected vertically up with an initial velocity of Vo . If the force due to the friction of the air is directly proportional to its instantaneous velocity,
Calculate the velocity and position of the particle as a function of time?

A stone of mass $10$g placed at the top of a tower $50$m high is allowed to fall freely. Show that law of conservation of energy is holds.

Explain conservative system and give examples

Explain conservative system and give examples

A car of mass 1 ton decelerates down an incline hill which makes an angle of 15⁰ to the valley below.
a)Find normal force
b)Calculate the frictional force acting on the mass.
c)What is the coefficient of the kinetic friction between the car and the road?
d)Calculate the cars deceleration.

Please show working out.
Thanks.

A particle Q of mass m falls under gravity in a medium, whose resistance to motion is of magnitude mkv^2, where v is the speed of Q and k is a positive constant. Given that the maximum speed of Q is U, show that U=√(g/k) (g is the acceleration due to gravity).
Given that Q is projected vertically upwards with speed V(>U), show that the speed of Q is equal to U when the height of Q above the point of projection is U^2/2g ln⁡[1/2 (1+V^2/U^2 )].
Find in terms of U, V and g, the time taken for the speed of Q to decrease from V to U.

A particle moves in a horizontal circular path of radius 2 m with uniform angular acceleration. It is observed to make 2 revolutions in the first 4 seconds of motion and 4 revolutions in the next 4 seconds. Find:
a) the initial angular velocity of the particle giving your answer in rad/s
b) the angular acceleration of the particle, giving your answer in rad per second squared.

If a 12 kg ball is rolled across the floor. It rolls for 5 meters before it reaches a stop. The ball feels a force of 15 N, what is the coefficient of friction on the floor? (Use g = 10m/s/s for this problem)

If a 12 kg ball is rolled across the floor. It rolls for 5 meters before it reaches a stop. The ball feels a force of 15 N, what is the coefficient of friction on the floor? (Use g = 10m/s/s for this problem)

Force acting on an object falling from a height close to the earth's surface is given as
F = -mg + bv ^ 2
The first term is the force of gravity, and the second is the friction force and b is a constant, and v is the velocity. The initial conditions are given as x0 = v0 = t0 = 0.
Find the position and velocity of the particle as a function of time. All intermediate actions should be clearly written.
Find the approximate values of position and velocity functions for small and large values of time t. All intermediate procedures must be written clearly.