I I K U N I V E R S I T Y

Departments of Electronics & Computer Science Engineering

Course: Engineering Physics I

Professors T. Yarman & E. Iksal

Final Exam: January 25, 2000

Question 1 (25 Points)

Consider a one-dimensional elastic scattering process, where a projectile of velocity v1i and mass m1, collides with a target of velocity v2i and mass m2. After the collision, the masses m1 and m2 acquire the velocities, respectively, v1f and v2f.

Order nowa) (10 p) Show that

b) (10 p) What is v2f ?

c) (5 p) What is approximately the “fractional decrease of the kinetic energy” (final kinetic energy) / (initial kinetic energy) of a tennis ball undergoing an elastic scattering with a wall?

Question 2 (10 Points)

A steel ball of mass m = 0.

5 kg is fastened to a cord L = 70 cm long and is fixed at the far end; it is released when the cord is horizontal. At the bottom of its path, the ball strikes a mass M = 2.5 kg steel block, initially at rest on a frictionless surface. The collision is elastic.

a) (5 p) What is the speed of the ball after the collision?

b) (5 p) What is the speed of the block after the collision?

Question 3 (25 Points)

One likes to measure the speed v of a bullet having a mass of m=10g, 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, 10m/s2.

b) (10 p) As the bullet flies through the block of wood, it is slown 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 v and H.

As usual, first establish your answer litterally; 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 mvi (the magnitude of which is mvi), 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 = v . (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 .