A body of mass 2 kg is dropped from a height of 20 m. It accelerates uniformly at the rate of 10 m/s2until it hits the ground. Calculate the initial momentum and the momentum just before it strikes the ground.
Answers
Given :
➳ Mass of body = 2kg
➳ Initial velocity = zero (freefall)
➳ Acc. due to gravity = 10m/s²
To Find :
➔ Initial momentum.
➔ Final momentum just before it strikes the ground.
SoluTion :
⇒ Momentum is defined adms the product of mass and velocity.
⇒ It is a vector quantity having both magnitude as well as direction.
⇒ SI unit : kg m/s or N s
⇒ For a body falling freely under the action of gravity, g is taken positive.
✴ Final velocity at which body hits the ground :
➠ v² - u² = 2gH
➠ v² - (0)² = 2(10)(20)
➠ v² = 400
➠ v = √400
➠ v = 20 m/s
✴ Initial momentum :
➛ Pi = m × u
➛ Pi = 2 × 0
➛ Pi = 0 Ns
✴ Final momentum :
⟶ Pf = m × v
⟶ Pf = 2 × 20
⟶ Pf = 40 Ns
Answer:
Mass - 2 kg
Height = 20 m
Gravity - 10 m/s²
Initial Momentum :
Since the Ball is in rest, the initial velocity of the ball will be 0 m / s. Hence we know that,
Initial Momentum = Mass * Initial Velocity ( u )
=> Initial Momentum = 2 kg * 0 m / s = 0 kg . m / s
Final Velocity ( v ) = √ ( 2gh )
Final Velocity = √ ( 2 * 10 * 20 )
Final Velocity = √ 400 => 20 m / s
Hence Final Momentum = Mass * Final Velocity ( v )
=> Final Momentum = 2 * 20
=> Final Momentum = 40 kg . m / s
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