two cars of equal mass with equal speeds traveling perpendicular to one another collide completely in elastically. what percentage of the cars' total energy is lost in the collision?
ritzi as in spikey sea urchins?
If a collision is elastic, no kinetic energy is lost. That is what an elastic collision means.
two cars of equal mass with equal speeds traveling perpendicular to one another collide completely inelastically. what percentage of the cars' total energy is lost in the collision?
If they stick together then momentum is conserved
x momentum before = m v
y momentum before = m v
x momentum after = 2 m U cos theta
y momentum after = 2 m U sin theta
so
2 U cos theta = v
2 U sin theta = v
or
cos theta = sin theta so theta = 45 degrees
cos theta = cos 45 = sqrt2/2 = sin theta
2 U = v/cos theta = 2 v /sqrt 2
so
U = v/sqrt 2
Ke before = 2 (1/2) m v^2 = m v^2
Ke after = (1/2) (2m) U^2 = m v^2/2
so half the Ke would be lost if there were no bounce at all
To determine the percentage of energy lost in the collision between two cars moving at equal speeds and with equal masses, you need to understand the concept of elastic collisions and the conservation of energy. Let's break down the steps on how to solve this problem:
1. Understand elastic collisions: In an elastic collision, both momentum and kinetic energy are conserved.
2. Calculate the initial kinetic energy: The kinetic energy of an object can be calculated using the formula: KE = 1/2 * m * v^2, where KE is the kinetic energy, m is the mass, and v is the velocity.
Since both cars have equal mass and equal speeds, their initial kinetic energies are the same. Let's denote it as KE_initial.
3. Calculate the final kinetic energy: After the collision, the kinetic energy may change due to energy transfer, so we need to calculate the final kinetic energy. Since the collision is completely inelastic, the cars stick together and move as one unit after the collision.
To find the final kinetic energy, we need to first calculate the final velocity of the combined mass. This can be done by using the conservation of momentum, as momentum is also conserved in elastic collisions. Since the cars are moving perpendicular to each other, the total momentum before the collision is zero.
4. Apply the conservation of momentum: Since momentum is conserved in collisions, we can write the equation: m1 * v1 + m2 * v2 = (m1 + m2) * v_f, where m1 and m2 are the masses of the cars, v1 and v2 are their initial velocities, and v_f is the final velocity after the collision.
Since both cars have equal masses and equal speeds, the equation becomes m * v + m * v = 2m * v_f. Simplifying further, we have 2mv = 2mv_f, which leads to v_f = v.
So, the final velocity after the collision is equal to the initial velocity of the cars.
5. Calculate the final kinetic energy: Now that we know the final velocity is the same as the initial velocity, we can calculate the final kinetic energy using the formula KE_final = 1/2 * (m1 + m2) * v_f^2.
Since the cars have equal masses, the equation becomes KE_final = m * v^2. Let's denote the final kinetic energy as KE_final.
6. Calculate the lost energy: The energy lost in the collision can be determined by subtracting the final kinetic energy from the initial kinetic energy: Lost energy = KE_initial - KE_final.
7. Calculate the percentage of energy lost: To find the percentage of energy lost, divide the lost energy by the initial kinetic energy and multiply by 100: Percentage of energy lost = (Lost energy / KE_initial) * 100.
Follow these steps with the given values of mass and speed to obtain the numerical answer to this problem.