Two balls have masses 44 kg and 86 kg. The 44 kg ball has an initial velocity of 80 m/s (to the right) along a line joining the two balls and the 86 kg ball is at rest. The 86 kg ball has initial velocity of −24 m/s. The two balls make a head-on elastic collision with each other.
(1)What is the final velocity of the 44 kg ball?
(2)The final velocity of the 86Kg ball?
Answer in units of m/s
you will have to use conservation of momentum; and energy. See this one as an example..
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Two balls have masses 44 kg and 86 kg. The 44 kg ball has an initial velocity of 80 m/s (to the right) along a line joining the two balls and the 86 kg ball is at rest. The 86 kg ball has initial velocity of −24 m/s. The two balls make a head-on elastic collision with each other.
(1)What is the final velocity of the 44 kg ball?
(2)The final velocity of the 86Kg ball?
Answer in units of m/s
To find the final velocities of the balls after the head-on elastic collision, we can use the principle of conservation of momentum and conservation of kinetic energy.
1) Conservation of momentum:
The total momentum before the collision is equal to the total momentum after the collision.
Momentum is calculated by multiplying the mass of an object by its velocity.
Before the collision:
Initial momentum of the 44 kg ball = mass × initial velocity = 44 kg × 80 m/s = 3520 kg*m/s
Initial momentum of the 86 kg ball = mass × initial velocity = 86 kg × (-24 m/s) = -2064 kg*m/s
After the collision:
Final velocity of the 44 kg ball = ?
Final velocity of the 86 kg ball = ?
To solve for the final velocities, we need to set up two equations using the conservation of momentum and conservation of kinetic energy.
2) Conservation of kinetic energy:
The total kinetic energy before the collision is equal to the total kinetic energy after the collision.
Before the collision:
Initial kinetic energy of the 44 kg ball = (1/2) × mass × (initial velocity)^2 = (1/2) × 44 kg × (80 m/s)^2
Initial kinetic energy of the 86 kg ball = (1/2) × mass × (initial velocity)^2 = (1/2) × 86 kg × (-24 m/s)^2
After the collision:
Final kinetic energy of the 44 kg ball = (1/2) × mass × (final velocity)^2
Final kinetic energy of the 86 kg ball = (1/2) × mass × (final velocity)^2
Now we have two equations:
Equation 1: Conservation of momentum
Momentum before collision = Momentum after collision
44 kg × 80 m/s + 86 kg × (-24 m/s) = 44 kg × final velocity of the 44 kg ball + 86 kg × final velocity of the 86 kg ball
Equation 2: Conservation of kinetic energy
Kinetic energy before collision = Kinetic energy after collision
(1/2) × 44 kg × (80 m/s)^2 + (1/2) × 86 kg × (-24 m/s)^2 = (1/2) × 44 kg × (final velocity of the 44 kg ball)^2 + (1/2) × 86 kg × (final velocity of the 86 kg ball)^2
We now have a system of two equations with two unknowns (final velocities of the balls). We can solve these equations simultaneously to find the values.
Alternatively, if you have access to a physics simulation software or an online momentum calculator, you can input the values and obtain the final velocities directly.