Croquet ball A moving at 8.0m/s makes a head on collision with ball B of equal mass and initially at rest. Immediately after the collision ball B moves forward at 7.1m/s .
What fraction of the initial kinetic energy is lost in the collision?
initial Ke calculate
final Ke, calculate
ke lost=initial-final
fractction lost=kelost/keinitial
To determine the fraction of the initial kinetic energy lost in the collision, we need to compare the initial kinetic energy of ball A with the final kinetic energy of both ball A and ball B combined.
The initial kinetic energy of ball A can be calculated using the formula:
Kinetic energy = (1/2) * mass * velocity²
Given that both ball A and ball B have equal mass, we can assume their mass, let's say, m.
The initial kinetic energy of ball A is:
KE_A = (1/2) * m * (8.0 m/s)² = 32 m
After the collision, ball B moves forward at 7.1 m/s. The final kinetic energy of both balls A and B combined can then be calculated by considering the final velocity of ball A, ball B, and their respective masses.
The final kinetic energy of ball A is:
KE_A_final = (1/2) * m * velocity_A² = (1/2) * m * (7.1 m/s)² = 25.315 m
The final kinetic energy of ball B is:
KE_B_final = (1/2) * m * velocity_B² = (1/2) * m * (7.1 m/s)² = 25.315 m
The total final kinetic energy of ball A and ball B is:
KE_final = KE_A_final + KE_B_final = 25.315 m + 25.315 m = 50.63 m
The fraction of initial kinetic energy lost in the collision can be calculated as:
Fraction lost = (Initial KE - Final KE) / Initial KE
= (KE_A - KE_final) / KE_A
= (32 m - 50.63 m) / 32 m
= -18.63 m / 32 m
≈ -0.582 m
Therefore, approximately 58.2% of the initial kinetic energy is lost in the collision.
To find the fraction of the initial kinetic energy lost in the collision, we need to compare the kinetic energy before and after the collision. The formula for kinetic energy is given by:
KE = 1/2 * m * v^2
where KE is the kinetic energy, m is the mass, and v is the velocity.
Let's denote the initial velocity of ball A as v1 = 8.0 m/s and the final velocity of ball B as v2 = 7.1 m/s.
The initial kinetic energy can be calculated using the formula:
KE_initial = 1/2 * m * v1^2
Similarly, the final kinetic energy can be calculated using the formula:
KE_final = 1/2 * m * v2^2
The fraction of the initial kinetic energy lost in the collision can be calculated as:
Fraction of energy lost = (KE_initial - KE_final) / KE_initial
Calculating the values plug in the given values:
v1 = 8.0 m/s
v2 = 7.1 m/s
Fraction of energy lost = (1/2 * m * v1^2 - 1/2 * m * v2^2) / (1/2 * m * v1^2)
Notice that the mass (m) cancels out when calculating the fraction of energy lost, so we don't need to know the mass.
Fraction of energy lost = (1/2 * v1^2 - 1/2 * v2^2) / (1/2 * v1^2)
Now, plug in the given values and calculate the fraction of energy lost.
(-2(vb)^2+2(va+vb))/va^2
where
va is first velocity and
vb is 2nd given velovty