A bullet, mass 10 g, is fired into a block of wood, mass 390 g, lying on a smooth surface. Then both (bullet & wood) move together with a velocity of 10 m/s. a) What was the speed of the bullet before collision? b) What is the K.E before and after the collision?
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Mass of bullet m1 = 10g
Mass of block m2 = 200g
Velocity of bullet before impact u1 = 500 m/s
Velocity of block before impact u2 = 0
Velocity of block+bullet after impact v = ?
Momentum before impact M1 = m1u1+m2u2
Or, M1 = m1u1 ------(1)
(since u2=0)
Momentum after impact M2 = m1v + m2v (since bullet gets embedded in block and both move with speed v)
Or, M2 = (m1+m2)v-----(2)
By conservation of momentum
M2 = M1-----(3)
From (1), (2) and (3)
(m1+m2)v = m1u1
Or, v = m1u1/(m1+m2)
= 10*500/(10+200) m/s
= 10*500/210 m/s
= 23.8 m/s
Ans: 23.8 m/s
Mass of block m2 = 200g
Velocity of bullet before impact u1 = 500 m/s
Velocity of block before impact u2 = 0
Velocity of block+bullet after impact v = ?
Momentum before impact M1 = m1u1+m2u2
Or, M1 = m1u1 ------(1)
(since u2=0)
Momentum after impact M2 = m1v + m2v (since bullet gets embedded in block and both move with speed v)
Or, M2 = (m1+m2)v-----(2)
By conservation of momentum
M2 = M1-----(3)
From (1), (2) and (3)
(m1+m2)v = m1u1
Or, v = m1u1/(m1+m2)
= 10*500/(10+200) m/s
= 10*500/210 m/s
= 23.8 m/s
Ans: 23.8 m/s
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