Answer:
Explanation:
Mass of bullet 30g=30/1000=0.03kg
Speed of bullet =390m/s
Mass of pendulum is 4kg
Total mass of bullet and pendulum, =4.03kg
Length of pendulum is L= 2.8m
Then, momentum is conserved
Momentum before collision = momentum after Collision
Mass of bullet ×Velocity of bullet=combine mass of bullet and pendulum × velocity of pendulum
0.03×390=4.03×V
V=0.03×390/4.03
V=2.9m/s
Then the Kinetic energy of pendulum is given as
K.E=½mv²
K.E=½×4.03×2.9²
K.E=16.95J
conservation of energy states that energy can neither be created nor destroy but can be transferred from one form to another.
Let acceleration due to gravity be
g=9.81m/s²
The vertical displacement of the pendulum (h)=?
Potential energy of the pendulum is given as
P.E=mgh
P.E=4.03×9.81×h
P.E=39.53h
So the P.E of the pendulum equals K.E of the pendulum
P.E=K.E
39.53h=16.95
h=16.95/39.53
h=0.43m
Knowing the height we can find the angle of the pendulum at the top of the swing:
θ=arcos(l-h)/l
θ=arcos(2.8-0.43)/2.8
θ=arcos(0.8464)
θ=32.2°
From A we get the displacement along the horizontal axis:
The maximum vertical displacement is
x=h Sinθ
x=0.43 Sin32.2
x=0.23m
So the displacement are (0.23,0.43)m
