Ball 1 is moving to the right at speed Vo when it collides with ball 2 - is initially at rest. After the collision, ball 1 's initial KE decreases by 80% and has a velocity at an angle of 40 degress below the horizontal.

Question

Ball 1 is moving to the right at speed Vo when it collides with ball 2 - is initially at rest. After the collision, ball 1 's initial KE decreases by 80% and has a velocity at an angle of 40 degress below the horizontal.

what fraction of the initial KE does ball 2 have after the collision?

Answer 1

To find the fraction of the initial kinetic energy (KE) that ball 2 has after the collision, we need to compare the final KE of ball 2 with its initial KE.

Let's denote the initial KE of ball 1 as KE1(initial) and the initial KE of ball 2 as KE2(initial).

Since ball 1's initial KE decreases by 80%, the final kinetic energy of ball 1, KE1(final), can be calculated as:

KE1(final) = KE1(initial) - 0.8 * KE1(initial)
= 0.2 * KE1(initial)

Now, we know that kinetic energy is proportional to the square of velocity. Therefore, if the initial velocity of ball 1 is Vo, the final velocity (V1(final)) of ball 1 can be calculated using the angle of 40 degrees below the horizontal.

For simplicity, let's disregard the horizontal and vertical components of the velocities and focus only on the magnitudes. The horizontal component of V1(final) can be calculated as:

V1(final) = Vo * cos(40)

Similarly, the vertical component of V1(final) can be calculated as:

V1(vertical final) = -Vo * sin(40)

During the collision, momentum is conserved. Therefore, the momentum of ball 1 after the collision, P1(final), can be calculated as:

P1(final) = m1 * V1(final)

Here, m1 is the mass of ball 1.

Since ball 2 is initially at rest and the collision is a two-body collision, the momentum of ball 2 after the collision, P2(final), is given by:

P2(final) = m2 * v2(final)

Here, m2 is the mass of ball 2.

Since momentum is conserved, we can equate P1(final) and P2(final) to find the final velocity of ball 2, v2(final):

P1(final) = P2(final)

m1 * V1(final) = m2 * v2(final)

Solving for v2(final), we get:

v2(final) = (m1 / m2) * V1(final)

Now, the final kinetic energy of ball 2, KE2(final), can be calculated using the formula:

KE2(final) = 0.5 * m2 * (v2(final))^2

Substituting the value of v2(final) and simplifying the expression, we have:

KE2(final) = 0.5 * m2 * [(m1 / m2) * V1(final)]^2
= (m1^2 / 2 * m2) * (V1(final))^2

Finally, let's calculate the fraction of the initial KE of ball 2:

Fraction of initial KE of ball 2 = KE2(final) / KE2(initial)

Where KE2(initial) is the initial kinetic energy of ball 2.

Therefore, to find the fraction of the initial KE that ball 2 has after the collision, you need to substitute the given values into the formulas and perform the necessary calculations.