A 0.300-kg ice puck, moving east with a speed of 5.86m/s , has a head-on collision with a 0.990-kg puck initially at rest. Assume that the collision is perfectly elastic.
What is the speed of the 0.300-kg puck after the collision?
What ise the speed of the 0.990-kg puck after the collision?
To find the velocities of the pucks after the collision, we can use the principle of conservation of momentum.
Conservation of momentum states that the total momentum of a system remains constant before and after a collision, provided no external forces act on the system.
The equation for conservation of momentum can be written as:
m1v1i + m2v2i = m1v1f + m2v2f
Where:
m1 and m2 are the masses of the pucks
v1i and v2i are the initial velocities of the pucks
v1f and v2f are the final velocities of the pucks
Given:
m1 = 0.300 kg
v1i = 5.86 m/s
m2 = 0.990 kg
v2i = 0 m/s (initially at rest)
We need to find v1f (final velocity of the 0.300-kg puck) and v2f (final velocity of the 0.990-kg puck).
First, let's use the conservation of momentum equation to solve for v1f:
m1v1i + m2v2i = m1v1f + m2v2f
Substituting the given values:
(0.300 kg)(5.86 m/s) + (0.990 kg)(0 m/s) = (0.300 kg)(v1f) + (0.990 kg)(v2f)
Now, we know that the collision is perfectly elastic, which means that kinetic energy is conserved as well. In an elastic collision, the total kinetic energy of the system before the collision is equal to the total kinetic energy of the system after the collision.
The equation for conservation of kinetic energy can be written as:
(1/2)m1(v1i)^2 + (1/2)m2(v2i)^2 = (1/2)m1(v1f)^2 + (1/2)m2(v2f)^2
Substituting the given values:
(1/2)(0.300 kg)(5.86 m/s)^2 + (1/2)(0.990 kg)(0 m/s)^2 = (1/2)(0.300 kg)(v1f)^2 + (1/2)(0.990 kg)(v2f)^2
Now we have a system of two equations with two unknowns: v1f and v2f. We can solve this system of equations simultaneously to find the final velocities of the two pucks after the collision.
By solving these equations, we find:
v1f ≈ 4.11 m/s
v2f ≈ 2.48 m/s
Therefore, the speed of the 0.30-kg puck after the collision is approximately 4.11 m/s, and the speed of the 0.99-kg puck after the collision is approximately 2.48 m/s.