Answer:
4 kg → +4 m/s
5 kg → -5 m/s
Explanation:
The law of conservation of momentum states that:
- m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'
- left side → velocities before collision
- right side → velocities after collision
You'll notice that we have two missing variables: v₁' & v₂'. Assuming this is a perfectly elastic collision, we can use the conservation of kinetic energy to set the initial and final velocities of the individual bodies equal to each other.
Let's substitute all known variables into the first equation.
- (4)(-6) + (5)(3) = (4)v₁' + (5)v₂'
- -24 + 15 = 4v₁' + 5v₂'
- -9 = 4v₁' + 5v₂'
Let's substitute the known variables into the second equation.
- (-6) + v₁' = (3) + v₂'
- -9 = -v₁' + v₂'
- 9 = v₁' - v₂'
Now we have a system of equations where we can solve for v₁ and v₂.
- -9 = 4v₁' + 5v₂'
- 9 = v₁' - v₂'
Use the elimination method and multiply the bottom equation by -4.
- -9 = 4v₁' + 5v₂'
- -36 = -4v₁' + 4v₂'
Add the equations together.
<u>The final velocity of the second body (5 kg) is -5 m/s</u>. Substitute this value into one of the equations in the system to find v₁.
- 9 = v₁' - v₂'
- 9 = v₁' - (-5)
- 9 = v₁' + 5
- 4 = v₁'
<u>The final velocity of the first body (4 kg) is 4 m/s.</u>
<u></u>
We can verify our answer by making sure that the law of conservation of momentum is followed.
- m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'
- (4)(-6) + (5)(3) = (4)(4) + (5)(-5)
- -24 + 15 = 16 - 25
- -9 = -9
The combined momentum of the bodies before the collision is equal to the combined momentum of the bodies after the collision. [✓]
Answer:
A.
Explanation:
momentum depends on weight and speed
What scientists use to make models of the Earth's water cycle so they can<span> see how it is ... Where </span>does<span> the water that we use to meet our everyday needs come from? .... what </span>you<span> notice about the </span>patterns<span> the</span>winds<span> and </span>clouds follow<span>: </span>Do clouds and<span> ... </span>same patterns<span>? </span>Can you find any patterns in the direction that they move? Precipitation is a vital component of how water moves through Earth’s water cycle, connecting
the ocean, land and atmosphere. Water evaporates from the surface of the land and oceans,
rises and cools, condenses into rain or snow, and falls again to the surface as precipitation. The
water falling on land collects in rivers and lakes, soil, and porous layers of rock, and much of it
flows back into the oceans. The cycling of water in and out of the atmosphere is a significant
aspect of the weather patterns on Earth. so that will be probs the best i can do
Answer:
Approximately (assuming that .)
Explanation:
Let denote the force that this spring exerts on the object. Let denote the displacement of this spring from the equilibrium position.
By Hooke's Law, the spring constant of this spring would ensure that .
Note that the mass of the object attached to this spring is . Thus, the weight of this object would be .
Assuming that this object is not moving, the spring would need to exert an upward force of the same magnitude on the object. Thus, .
The spring in this question was stretched downward from its equilibrium by:
.
(Note that is negative since this displacement points downwards.)
Rearrange Hooke's Law to find in terms of and :
.