A mass of 12kg at rest explodes into two pieces of masses 4kg and 8kg which move in opposite directions. If the velocity of 8 pieces is 6 m/s , then the kinetic energy of other piece is , in joules is _?
Answers
We know that by the law of Conservation of Energy ,
initial momentum = final momentum .
Here , the momentum is the product of the mass and velocity .
Initial momentum refers to the product of mass and initial velocity .
Final momentum refers to the product of mass and final velocity .
The initial velocity of the object was zero .
The initial mass of the object was also zero .
m = 12 kg .
v = 0 m/s .
Let the momentum gained by the 4 kg object be x .
Then the momentum will be 4 x kg .
The momentum of the 8 kg piece is given as 6 m/s .
Hence the momentum is 8 kg × 6 m/s ⇒ 48 kg m/s .
Final momentum = initial momentum .
⇒ 12 kg × 0 m/s = ( 4 x kg ) + ( 48 kg )
⇒ 4 x kg = - 48 kg m/s
⇒ 4 x = - 48 m/s
⇒ x = - 48/4 m/s
⇒ x = - 12 m/s .
This indicates that the velocity is in opposite direction against that 8 kg .
Kinetic energy = 1/2 m v²
m = 4 kg [ given ]
v = ( -12 ) m/s .
K = 1/2 × 4 kg × ( -12 m/s )²
⇒ K = 2 kg × 144 m²/s²
⇒ K = 288 J
The kinetic energy of the other piece will be 288 J .
Answer:
By law of conservation of moment conservation:
initial momentum =final momentum
12 x 0 = (4xv) + (8 x6)
So v= 48/4 =12m/s
Hence the piece having 4kg mass will move with 12m/s in opposite direction of the piece having mass 8kg
now the KE of 4kg piece= 12x(mv^2) =(1/2)x 4 x 12^2 = 288J