A perfectly elastic collision between two colliding objects of masses m₁ and m₂ is a collision that conserves both the quantity known as the total linear momentum and the quantity known as the total kinetic energy. For a perfectly elastic collision between mass m₁ moving at speed v₁; and mass m₂ moving at speed v2; prior to the collision, the conservation of total linear momentum is expressed as: m₁v₁i + m₂v2i = m₁v₁f + m2 V2 f and the conservation of total kinetic energy is expressed as: 1 1 1 1 m₁(v₁)² + m₂(v₂)² = _m₁(0₁) ² + + m²(v₂1)²2 2 where Vif and V2f are the speeds of the masses, respectively, after the collision event. Part (a) Determine vif and V2f in terms of m₁, 22, U1i, U2i. Part (b) If m₁ = m₂ and v₁i = 5 [m/s] and mass 2 is initially at rest (i.e., a stationary target), find the direction and the speed of each mass after the collision. Part (c) If m₁ = m2, v₁i = 5 [m/s] and v2i = -5 [m/s] so that the two masses are initially moving toward each other with equal speed, find the direction and the speed of each mass after the collision.
A perfectly elastic collision between two colliding objects of masses m₁ and m₂ is a collision that conserves both the quantity known as the total linear momentum and the quantity known as the total kinetic energy. For a perfectly elastic collision between mass m₁ moving at speed v₁; and mass m₂ moving at speed v2; prior to the collision, the conservation of total linear momentum is expressed as: m₁v₁i + m₂v2i = m₁v₁f + m2 V2 f and the conservation of total kinetic energy is expressed as: 1 1 1 1 m₁(v₁)² + m₂(v₂)² = _m₁(0₁) ² + + m²(v₂1)²2 2 where Vif and V2f are the speeds of the masses, respectively, after the collision event. Part (a) Determine vif and V2f in terms of m₁, 22, U1i, U2i. Part (b) If m₁ = m₂ and v₁i = 5 [m/s] and mass 2 is initially at rest (i.e., a stationary target), find the direction and the speed of each mass after the collision. Part (c) If m₁ = m2, v₁i = 5 [m/s] and v2i = -5 [m/s] so that the two masses are initially moving toward each other with equal speed, find the direction and the speed of each mass after the collision.
Related questions
Question
![A perfectly elastic collision between two colliding objects of masses m₁ and m₂ is a collision that conserves
both the quantity known as the total linear momentum and the quantity known as the total kinetic energy.
For a perfectly elastic collision between mass m₁ moving at speed v₁; and mass m₂ moving at speed v2; prior
to the collision, the conservation of total linear momentum is expressed as:
m₁v₁i + m₂v₂i = m₁v₁f + m2 V2 f
and the conservation of total kinetic energy is expressed as:
1
1
1
m₁(v₁i)² + ½ m2(v2;)² = = m₁(v₁ƒ)² + 21/1m2 (v21) ²
2
where Vif and V2f are the speeds of the masses, respectively, after the collision event.
Part (a) Determine vif and V2f in terms of m₁, 22, Vli, V2i.
Part (b) If m₁ = m₂ and v₁i = 5 [m/s] and mass 2 is initially at rest (i.e., a stationary target), find the
direction and the speed of each mass after the collision.
Part (c) If m₁ = m2, v₁i = 5 [m/s] and v2i = -5 [m/s] so that the two masses are initially moving toward
each other with equal speed, find the direction and the speed of each mass after the collision.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4d03641-6675-4e75-b9b2-0b70f26b5416%2Fffd1b616-eae0-4382-be9a-4632b9ba9f2a%2Fo5l1p7c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A perfectly elastic collision between two colliding objects of masses m₁ and m₂ is a collision that conserves
both the quantity known as the total linear momentum and the quantity known as the total kinetic energy.
For a perfectly elastic collision between mass m₁ moving at speed v₁; and mass m₂ moving at speed v2; prior
to the collision, the conservation of total linear momentum is expressed as:
m₁v₁i + m₂v₂i = m₁v₁f + m2 V2 f
and the conservation of total kinetic energy is expressed as:
1
1
1
m₁(v₁i)² + ½ m2(v2;)² = = m₁(v₁ƒ)² + 21/1m2 (v21) ²
2
where Vif and V2f are the speeds of the masses, respectively, after the collision event.
Part (a) Determine vif and V2f in terms of m₁, 22, Vli, V2i.
Part (b) If m₁ = m₂ and v₁i = 5 [m/s] and mass 2 is initially at rest (i.e., a stationary target), find the
direction and the speed of each mass after the collision.
Part (c) If m₁ = m2, v₁i = 5 [m/s] and v2i = -5 [m/s] so that the two masses are initially moving toward
each other with equal speed, find the direction and the speed of each mass after the collision.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 5 steps with 5 images
