Question

6. A shell is fired from a gun with a muzzle velocity of 20.0 m's, at an angle of 60.0 with the horizontal. At the top of the trajectory, the shell explodes into two fragments of equal mass. One fragment, whose speed immediately after the explosion is zero, falls vertically. How far from the gun does the other fragment land, assuming that the terrain is level and that the air drag is negligible? (You may use R-(v/g) sin(20) 7. In figure 1 below the angular velocity is given as a function of time for a rotating disk, rotating about its central axis. For a point on the rim of the disk, rank the four instants a, b, c, and d according to the magnitude of the tangential acceleration and the radial acceleration, from greatest to least fig.l 8. A block of mass M, at rest on a horizontal frictionless table, is attached to a rigid support by a spring of constant k. A bullet of mass m and velocity v strikes the block horizontally and embeds into the block. Determine the equations of motion for the resulting simple harmonic oscillations. What fraction of the original kinetic energy of the bullet appears as mechanical energy in the harmonic oscillator? What is the total energy of the oscillating system and from where did the energy come? 9. What is the minimum area of the top surface of a slab of ice 0.30 m thick floating on fresh water that will hold up an automobile of mass 1100 kg? Does it matter where the car is placed on the block of ice? (The density of water- 1000 kg/m', the density of ice-917 kg/m.) 10. You place one half gallon of water in a microwave oven that has a power output of 1500 W. The water is from the tap which has a temperature of 67 °C. How long does it take to boil all of the water into steam, assuming that the whole process occurs very near equilibrium? (I m 264 gal, Cwater 4190 J/kg K, L-2256 kJ/kg)

Answer 1

6. Here after it explodes the velocity of the moving fragment lets, v₁ , so from momentum conservation we get

$Mv=\frac{M}{2}\times 0+\frac{M}{2}v_{1}$

$v_{1}=2v$

so maximum distance travelled,

1.5×202sin 1200 9.8 3føǐn2θ = 53.02772