In: Physics
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.
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.