A 120 kg mass is blown apart into an 80 kg piece and 40 kg piece. after the blast, the two masses are moving apart with a relative velocity of 60 m/s. the total kinetic energy after the explosion is:
A. 21 kJ
B. 35 kJ
C. 48 kJ
D. 56 kJ
E. 82 kJ
Because of momentum conservation rules, the two pieces must go in opposite directions with
V2 = 2 V1
V1 is the final speed of the 80 kg piece; V2 is the final speed of the 40 kg piece.
Furthermore, because of the relative velocity that was given,and the opposite directions of motion,
V1 + V2 = 60 m/s
V1 + 2V1 = 60
V1 = 20 and V2 = 40 m/s
Now compute KE = (M1/2) V1^2 + (M2/2) V2^2
and see which answer is correct.
48000
To find the total kinetic energy after the explosion, we need to calculate the kinetic energy of each piece separately and then add them together.
Given information:
Mass of the first piece (M1) = 80 kg
Mass of the second piece (M2) = 40 kg
Final speed of the first piece (V1) = 20 m/s
Final speed of the second piece (V2) = 40 m/s
The formula to calculate kinetic energy is KE = (1/2) * mass * velocity^2.
Now let's calculate the kinetic energy of each piece:
KE1 = (1/2) * M1 * V1^2
= (1/2) * 80 * 20^2
= 16000 J
KE2 = (1/2) * M2 * V2^2
= (1/2) * 40 * 40^2
= 16000 J
Total kinetic energy = KE1 + KE2
= 16000 + 16000
= 32000 J
Now, let's convert the total kinetic energy from joules (J) to kilojoules (kJ):
Total kinetic energy = 32000 J
= 32 kJ
None of the given answer choices match the calculated total kinetic energy of 32 kJ. Therefore, none of the provided answer choices are correct.
To calculate the total kinetic energy after the explosion, we can use the formula:
KE = (M1/2) V1^2 + (M2/2) V2^2
Given the masses and velocities:
M1 = 80 kg
M2 = 40 kg
V1 = 20 m/s
V2 = 40 m/s
Plugging the values into the formula, we get:
KE = (80/2) * (20^2) + (40/2) * (40^2)
Calculating the values:
KE = 40 * 400 + 20 * 1600
KE = 16000 + 32000
KE = 48000 J
Converting the answer to kJ:
KE = 48000 J = 48 kJ
Therefore, the correct answer is C. 48 kJ.