Classical Mechanics Answers

A horizontal spring-mass system oscillates on a frictionless table. If the ratio of the mass to the spring constant is 0.037 kg·m/N, and the maximum speed of the mass was measured to be 4.5 m/s, the maximum extension of the spring will be  cm.

1. Prove that the area of a parallelogram with sides A and B is |A×B|. 

1. 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?   

1. A spaceship of mass m has velocity v in the positive x direction of an inertial reference frame. A mass dm is fired out the rear of the ship with constant exhaust velocity (-v0) with respect to the spaceship. a) using conservation of momentum, show that dv/v0 = dm/m, b) By integration, find the dependence of v on m if v1 and m1 are the initial values. c) Can the acceleration be constant if dm/dt, the burning rate is constant. 

A rocket has an initial mass of 2 x 104 kg, a mass ratio of 3, a burning rate of 100 kg/sec, and an exhaust velocity of 980 m/sec. The rocket is fired vertically from the surface of the earth. How long after ignition of the engines will the rocket leave the ground?  (R1P14-3, 493)

1. A ball is thrown upward from the top of a 35-m tower, with an initial velocity of 80 m/s and an angle of 25 degree. a) Find the time to reach the ground and the distance R from the bottom of the tower to the point of impact in the figure below. b) Find the magnitude and direction of the velocity at the moment of impact.  

1. A particle of mass m =2kg starts from rest at the origin of an integral coordinate system at time t=0. A force F = 2 i + 4t j + 6t2 k is applied to it. Find the acceleration, velocity, and position of the particle for any latter time.

For the 2P → 1S transition in the hydrogen atom calculate ω. Assuming the 

spontaneous emission lifetime of the 2P state to be 1.6 ns, calculate the Einstein B 

coefficient. Assume n0 ≈1.

1. Show that the rate of change of the total angular momentum of a system of particles is equal to the resultant torque exerted by all external forces which act on the system. 

1. Show that the rate of change of the total angular momentum of a system of particles is equal to the resultant torque exerted by all external forces which act on the system.