Mechanics | Relativity Answers

A particle of mass m, traveling at a velocity vi, strikes a stationary second object of mass

2m, and the two of them scatter at different angles to the initial direction. The incoming

particle scatters at an angle of cos 3 2 5 1

1

   . This collision is inelastic, with exactly

half of the incoming kinetic energy being lost in the collision. Determine the final velocities

of both particles in terms of vi only.

N/B Leave your answers in exact form. e.g. 2 rather than 1.414… [10]

ii) The weight on a vertical spring undergoes forced vibrations according to the 

following equation:

d2x/dt2 +4x=8sin wt

where x is the displacement from the equilibrium position and  > 0 is a constant. 

If at t = 0, x = 0 and 

dt/dx=0

, calculate x as a function of t.

A treasure map required that the seekers, starting from a certain point X, walk 10 m due North, then 17 m due East followed by 25 m due South. Determine the magnitude and the direction of the treasure seekers starting point.

A sphere of mass 12kg and another one of mass 8 kg are moving towards each other in a smooth linear groove. The speed of the heavier sphere is 3 times that of the lighter sphere . After collision the heavier sphere has a speed of 4/1/6 m/s and the lighter sphere a speed of 6m/s . Calculate the speeds of the sphere before collisions

Two bodies A and B of equal masses moving with velocities (10km/s, 030°) and (15km/s, 090°) impinges and coalesced. Find the initial velocity with which the composite body begins to move immediately after the collision

The mass of a cork is 2g.What is the fraction o

f the cork is immersed when it floats in water

With what impulse does a 0.50kg newspaper have to be thrown to give it a velocity of 3 m/s

A spaceship of rest length 100 m takes 4 µs to pass a stationary observer on earth. Determine the ship’s velocity relative to the earth.

Describe, in terms of momentum of the molecules, how a pressure is exerted on the walls of the cylinder.

.There is a node, starting at (0, 0, 0), and it's moving 10 per second on the X axis, 6 per second on the Y axis, and 8 per second on the Z axis. Please answer the follow questions.

(1) What is the motion equation of this node?

(2) what is the position of this node after 5 seconds?