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Elis [28]
3 years ago
8

a bullet moving with a velocity of 100m/s pierce a block of wood and moves out with a velocityof 10 m/s.if the thickness of the

block reduces to one half of the previous value .what will be the emerging velocity of bullet?
Physics
1 answer:
erma4kov [3.2K]3 years ago
3 0

The emerging velocity of the bullet is <u>71 m/s.</u>

The bullet of mass <em>m</em> moving with a velocity <em>u</em>  has kinetic energy. When it pierces the block of wood, the block exerts a force of friction on the bullet. As the bullet passes through the block, work is done against the resistive forces exerted on the bullet by the block. This results in the reduction of the bullet's kinetic energy. The bullet has a speed <em>v</em> when it emerges from the block.

If the block exerts a resistive force <em>F</em> on the bullet and the thickness of the block is <em>x</em> then, the work done by the resistive force is given by,

W=Fx

This is equal to the change in the bullet's kinetic energy.

W=Fx=\frac{1}{2} m(u^2-v^2)......(1)

If the thickness of the block is reduced by one-half, the bullet emerges out with a velocity v<em>₁.</em>

Assuming the same resistive forces to act on the bullet,

F(\frac{x}{2} )=\frac{1}{2} m(u^2-v_1^2)......(2)

Divide equation (2) by equation (1) and simplify for v<em>₁.</em>

\frac{\frac{Fx}{2} }{Fx} =\frac{(u^2-v_1^2)}{(u^2-v^2)} \\\frac{100^2-v_1^2}{100^2-10^2} =\frac{1}{2} \\v_1^2=5050\\v_1=71.06 m/s

Thus the speed of the bullet is 71 m/s


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You are working as a summer intern for the Illinois Department of Natural Resources (DNR) and are assigned to some initial work
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1)   F = 71.6 N , 2)    F = 120.2 N , 3)  P_m=  68.600 Pa, 4)  V = 2.4210-5 m³

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The pressure is given by the expression

         P = P_atm + ρ g h

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       P = P_atm

we substitute in the expression of force

         F = P_atm π d² / 4

         

let's calculate

         F = 1,013 10⁵ π 0.03²/4

         F = 7.16 10¹ N

         F = 71.6 N

2) the force on the inner side

  the pressure

       P = P_atm + ρ g h

       P = 1,015 10⁵ + 1,000 9.8 7

        P = 1,701 10⁵ Pa

        F = 1,701 10⁵ π 0.03² / 4

        F = 1,202 10²

        F = 120.2 N

3) manometric pressure

       Pm = ρ g h

       P m = 1000 9.8  7

       P_m=  68.600 Pa

4) In this part they ask for the volume that comes out in time t= 3 h

   to calculate this volume we can use the flow ratio

         Q = A v

          V t = A v

          V = A v / t

sent is the velocity of the water that comes out, to calculate it we use the Bernoulli equation

we will use index 1 for the lake surface and ionice 2 apa the position of the plug

           P₁ + ρ g v₁² + ρ g y₁ = P₂ + ρ g v₂² + ρ g y₂

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