Answer:
a) p(total) = <0.05, 0.1, 0.1 > kg m/s
b) p = <0.05, 0.1, 0.1 > kg.m/s
c) v_f = < 1, 2, 2 > m/s
Explanation:
a.)
Mass of each lump = 25 g = 0.025 kg
Velocity of lump 1 = < -2, 0, -7 > m/s
Momentum of lump 1 = Mass×Velocity
= 0.025×< -2, 0, -7 >
= < -0.05, 0, 0.175> kg m/s
Velocity of lump 2 = < 4, 4, -3 > m/s
Momentum of lump 2 = Mass×Velocity
= 0.025×< 4, 4, -3 >
= < 0.1, 0.1, -0.075> kg m/s
Total momentum before impact = < -0.05, 0, 0.175 > + < 0.1, 0.1, -0.075>
= < 0.05, 0.1, 0.1 > kg m/s
⇒p(total) = <0.05, 0.1, 0.1 > kg m/s
b)
As we know that,
By the law of conservation of linear momentum,
The total momentum will be the same before and after the collision.
⇒Momentum of the stuck together after the collision = Total momentum of the lumps just before impact.
⇒ p = <0.05, 0.1, 0.1 > kg m/s
c)
Let the final velocity = v_f
Total mass = 0.025 + 0.025 = 0.05 kg
As
Momentum = mass ×velocity
⇒ <0.05, 0.1, 0.1 > = 0.05 ×v_f
⇒ v_f = <0.05, 0.1, 0.1 > / 0.05
= < 1, 2, 2 > m/s
⇒v_f = < 1, 2, 2 > m/s
