Mass M 2 5 Kg Steel Block example essay topic
Question 3 (25 Points) One likes to measure the speed vs. of a bullet having a mass of m = 10 g, with the aid of a ballistic pendulum. The mass of the large block of wood of the pendulum is M = 5 kg. Thus, the bullet is fired and the block+bullet combination swings upward with a velocity V, its center of mass rising a vertical distance h = 6 cm, before the pendulum comes to rest at the end of its arc. a) (10 p) You shall now apply the law of conservation of momentum during the collision of the bullet and the pendulum, and the law of conservation of mechanical energy in the swinging process of the pendulum, in order to find the speed of the bullet. Thus express v, in terms of M, m, h and, g, earth's gravitational acceleration, to be approximately taken, 10 m /'s 2. b) (10 p) As the bullet flies through the block of wood, it is slow down; its energy is converted into heat.
Now suppose that the initial kinetic energy of the bullet is transformed into just the 'heat' it deposits into the block of wood, and the 'swinging energy' of this block. Thus show that the heat deposited by the bullet into the block of wood, can be approximately expressed as. Note thus that practically, the entire initial kinetic energy of the bullet has gone into heat, within the block of wood. c) (5 p) Find numerically vs. and H. As usual, first establish your answer literally; only then, do the numerical application; be sure that you use coherent units. Question 4 (20 Points) According to Newton's Second Law, with the familiar notation, , (1) where F is the force vector, the change in the momentum p, through the interval of time, .
Now suppose that a steady stream of n particles per second, with identical linear momentum of mv i (the magnitude of which is mv i), collides with a body B, which is fixed in place. The colliding particles are bounced back with a velocity vf. Through collisions of this one dimensional situation, the impulse acting on the body B carried by each particle, is by definition, m (vf - vi). a) (5 p) Express in terms of n, m, vf, and vi. b) (10 p) Suppose that vi = vf = vs. (1) Thus show that, F in this case, can be written as F. (2) d) (5 p) It is well known that bullets and other missiles fired at Superman, simply bounce off his chest. Suppose that a gangster sprays Superman's chest with 5 g bullets at the rate of 200 bullets / min, the speed of each bullet being 1000 m / 's. We suppose that the bullets rebound straight back with no change in speed. What is the average force exerted by the stream of bullets on Superman's chest?
Question 5 (20 Points) a) (10 p) The moon is about 300 000 km away from Earth. What is then its speed of rotation (v) around our planet? b) (10 p) What is the moon's angular velocity around Earth? The universal constant is given to be G = 6.67 x 10-11 MKS, and Earth's mass is M = 6 x 1024 kg..