Question

In: Physics

A bullet of mass m=11 gr is fired into a block of mass M=1 kg initially...

A bullet of mass m=11 gr is fired into a block of mass M=1 kg initially at rest at the edge of a frictionless table of height h=1.10 m. The bullet remains in the block and the block lands a distance d=0.67 m from the bottom of the table.

a)Determine the initial velocity of the bullet.

b) Determine the loss of kinetic Energy during the collision.

Solutions

Expert Solution

Part A.

First calculate the initial speed of projectile motion when Block+Bullet starts falling

Since there is no initial vertical velocity for Bullet + Block, So Using 2nd kinematic equation:

h = V0y*t + (1/2)*a*t^2

h = vertical distance traveled = -1.10 m

V0y = 0 m/sec, Since initial velocity is only in horizontal direction

a = Vertical acceleration = -g = -9.81 m/sec^2

So,

-1.10 = 0 + (1/2)*(-9.81)*t^2

t = sqrt (2*1.10/9.81) = 0.47356 sec

Now range in projectile motion is given by:

R = V0x*t

R = horizontal distance traveled by block + bullet = d = 0.67 m

V0x = Initial speed of block + bullet = R/t

V0x = 0.67/0.47356 = 1.4148 m/sec

Now Using momentum conservation on block + bullet before and after collision

Pi = Pf

mb*vb + Mb*Vb = (mb + Mb)*V0x

mb = mass of bullet = 11.0 gm = 0.011 kg

Mb = mass of block = 1 kg

Vb = initial speed of block = 0 m/sec

vb = initial speed of bullet = ?

So,

vb = (mb + Mb)*V0x/mb

vb = (0.011 + 1)*1.4148/0.011 = 130.033 m/s

vb = Initial speed of bullet = 130.0 m/sec

Part B.

Now loss of kinetic energy during the collision will be:

dK = KEi - KEf

dK = (1/2)*mb*vb^2 + (1/2)*Mb*Vb^2 - (1/2)*(mb + Mb)*V0x^2

Using known values:

dK = (1/2)*0.011*130.033^2 + (1/2)*1*0^2 - (1/2)*(0.011 + 1)*1.4148^2 = 91.985 J

dK = 92.0 J = Loss in kinetic energy

Let me know if you've any query.


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