an object of mass 1 kg travelling a straight line with a velocity of 10 metre per second collides with straight to the stationary old block of a 5 kg mass then the both of together in their same straight line calculate the total momentum just before the impact of a just after the impact calculate the velocity of combine object
Answers
Answer:
Mass of the object, m1 = 1 kg
Velocity of the object before collision, v1 = 10 m/s
Mass of the stationary wooden block, m2 = 5 kg
Velocity of the wooden block before collision, v2 = 0 m/s
ˆ´ Total momentum before collision = m1 v1 + m2 v2
= 1 (10) + 5 (0) = 10 kg m sˆ’1
It is given that after collision, the object and the wooden block stick together.
Total mass of the combined system = m1 + m2
Velocity of the combined object = v
According to the law of conservation of momentum:
Total momentum before collision = Total momentum after collision
m1 v1 + m2 v2 = (m1 + m2) v
1 (10) + 5 (0) = (1 + 5) v
v = 10 / 6
= 5 / 3
The total momentum after collision is also 10 kg m/s.
Total momentum just before the impact = 10 kg m sˆ’1
Total momentum just after the impact = (m1 + m2) v = 6 — 5 / 3 = 10 kg ms-1
Hence, velocity of the combined object after collision = 5 / 3 ms-1
Given :-
Mass of the object = 1 kg
Mass of the old block = 5 kg
Velocity of the object = 10 m/s
Velocity of the old block = 0 m/s
To Find :-
The momentum after collision.
The velocity of the combined object after collision.
Solution :-
We know that,
- m = Mass
- p = Momentum
- v = Velocity
Moving together after collision,
Total mass = m₁ + m₂
Given that,
Mass₁ = 1 kg
Mass₂ = 5 kg
Substituting their values,
⇒ 1 + 5
⇒ 6 kg
Momentum before collision,
Momentum before collision = Momentum of object + Momentum of block
Substituting their values,
⇒ (1 × 10) + (5 × 0)
⇒ 10 + 0
⇒ 10 kg m/s
Therefore, the momentum before collision is 10 kg m/s.
Momentum after collision,
Momentum = Mass × Velocity
Given that,
Mass (m) = 6 kg
Velocity (v) = v
Substituting their values,
⇒ (m₁ + m₂) × v
⇒ 6 × v
⇒ 6v
According to the question,
Total momentum before collision = Total momentum after collision
Given that,
Momentum before collision = 10 kg m/s
Momentum after collision = 6v
Substituting their values,
⇒ 10 = 6v
⇒ v = 10/6
⇒ v = 5/3 m/s
Therefore, the velocity of the combined object after collision is 5/3 m/s.
Momentum before collision = momentum after collision
Substituting their values,
10 = 10
Therefore, the momentum after collision is 10 kg m/s.
Additional knowledge :-
Linear momentum:
Linear momentum is defined as the vector quantity. A body’s momentum is always in the same direction as its velocity vector.
The SI unit of linear momentum is kg m/s.
Formula: Momentum = Mass × Velocity
Where,
➡ M = Mass
➡ P = Momentum
➡ V = Velocity