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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.

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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.
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.
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