A bullet of mass 0.012 kg and horizontal speed 70 m/s strikes a block wood of mass 0.4 kg and instantly comes to rest with respect to block. The block is suspended from the ceiling by means of thin wire. Calculate the height to which the block rises.
Answers
Answer:
Mass of the bullet, m = 0.012 kg
Initial speed of the bullet, u
b
=70m/s
Mass of the wooden block, M=0.4 kg
Initial speed of the wooden block, u
B
=0
Final speed of the system of the bullet and the block = v m/s
Applying the law of conservation of momentum:
mu
b
+Mu
B
=(m+M)v
0.012×70+0.4×0=(0.012+0.4)v
v=0.84/0.412
=2.04 m/s
For the system of the bullet and the wooden block:
Mass of the system, m
′
=0.412 kg
Velocity of the system =2.04m/s
Height up to which the system rises = h
Applying the law of conservation of energy to this system:
Potential energy at the highest point = Kinetic energy at the lowest point
m
′
gh=(1/2)m
′
v
2
h=
2g
v
2
=
2×9.8
(2.04)
2
=0.2123m
The wooden block will rise to a height of 0.2123m.
The heat produced = Kinetic energy of the bullet - Kinetic energy of the system
=(1/2)mu
2
−(1/2)m
′
v
2
=(1/2)×0.012×(70)
2
−(1/2)×0.412×(2.04)
2
=29.4−0.857=28.54J
Answer:
28.54 J
mass of bullet (m)=0.012 Kg
initial speed of bullet (Ub)= 70 m/s
mass of wooden block (M)= 0.4 Kg
initial speed of wooden block (UB) =0
using law conversation of momentum.
mUb + MUB = ( m + M ) V
0.012 × 70 + 0.4 ×0 =( 0.012 + 0.4 ) V
V = 0.84/0.412
V = 2.04 m/s
mass of system (m') = 0.412 Kg
velocity of system = 2.04 m/s
height up to which system rises = h
potential energy at highest point = kinetic energy at lowest point
m'gh = (1/2) m'v²
h=(1/2)v²/g
by substituting the value we get the answer
= 0.2123 m
heat produced = kinetic energy of bullet - kinetic energy of system
= (1/2) mu² - (1/2) Mv²
= 29.4 - 0.857
= 28.54 J
.
I hope this helps you.......
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