Answer:
energy loss due to friction and the impacts = 2.97 J; The impact loss due to AB impacting the carrier is =25.72J; The impact loss at first impact is 6,316.64J
Explanation:
First find the velocity of the bullet after the first impact using
M1V1 + 0 = (M1 + M2)v'
Where M1 is the mass of the bullet
M2 is the mass of the block B
M3 is the mass of the carrier
v' is the velocity
v' = M1V1/(M1 + M2)
v'= (30 × 10^-3 kg)(460 m/s) / (30 × 10^-3 kg + 3 kg)
v' = 13.8/3.03
v'= 4.55m/s
Also calculate final velocity of the carrier v2'
v2' = M1V1/(M1 + M2 + M3)
v2'= (30 × 10 kg)(460 m/s) / (30 × 10 kg + 3 kg + 30kg)
v2' =0.42m/s
Now to calculate energy loss due to friction
Normal force
N= W1 + W2 = (m1 + m2)g
Where W1 and W2 is the weight of the bullet and block respectively
g is gravitational acceleration for taken as 9.81m/s
= (0.030 kg + 3 kg)(9.81 m/s) 29.724 N
Friction force = coefficient of kinetic× normal force
Where coefficient of kinetic = 0.2
Ff = (0.2)(29.724)= 5.945 N
Now
Energy loss due to friction = frictional force × distance
Assume distance is 0.5 m.
Energy loss due to friction = 5.945 N × 0.5 m
= 2.97J
Kinetic energy of block with embedded bullet immediately after first impact:
1/2 × (m1 + m2)(v')^2
1/2 × (30 × 10^-3 kg + 3 kg)(4.55m/s)^2
= 1/2 × (3.03kg) × (4.55m/s)^2
= 31.36 J
Final kinetic energy of bullet, Block, and Carrier together
1/2 × (m1 + m2 + m3)(v2')^2
1/2 × (30 × 10^-3 kg + 3 kg + 30kg) (0.42m/s)^2
1/2 × (33.03kg) × (0.42m/s)^2
= 2.91 J
Therefore
Loss due to friction and stopping impact = Kinetic energy of block with embedded bullet immediately after first impact - Final kinetic energy of bullet, Block, and Carrier together
= 31.36 J - 2.91 J
= 28.69 J
Impact loss due to AB impacting the carrier = loss due to friction- energy due to friction
28.69J - 2.97J
=25.72J
Initial kinetic energy of system ABC = 1/2(m1vo)
=1/2(0.030 kg)(460 m/s)^2 = 6,348J
Therefore
Impact loss at first impact = Initial kinetic energy of system ABC - Kinetic energy of block with embedded bullet immediately after first impact:
= 6,348J - 31.36 J
= 6,316.64J
