Question

Impact extinction 65 million years ago over 50% of all species became extinct, ending the reign of dinosaurs and opening the way for mammals to become the dominant land vertebrates. A theory for this extinction, with considerable supporting evidence, is that a 10-km-wide 1.8×1015kg asteroid traveling at speed 11 km/s crashed into Earth.

A) Determine the change in velocity of Earth due to the impact. Mass of Earth is 5.98×1024kg.

B) Determine the average force that Earth exerted on the asteroid while stopping it. Assume that stopping distance is 0.60 km (depth of the crater created)

C) Determine the internal energy produced by the collision (a bar chart for the process might help). By comparison, the atomic bombs dropped on Japan during World War II were each equivalent to 15,000 tons of TNT (1 ton of TNT releases 4.2×109J of energy).

Answer 1

The change in velocity of Earth due to the impact can be calculated using the conservation of momentum. The average force exerted by Earth on the asteroid can be determined using the concept of impulse. The internal energy produced by the collision can be calculated by subtracting the initial kinetic energy from the final kinetic energy.

Step-by-step explanation:

A) To determine the change in velocity of Earth due to the impact, we can use the principle of conservation of momentum. The momentum of the asteroid before the impact is given by its mass multiplied by its velocity (p1 = m1v1), and the momentum of the Earth after the impact is given by the mass of the Earth multiplied by its final velocity (p2 = m2v2). Since momentum is conserved, we can equate the two momentum expressions: p1 = p2. Here's how to calculate the change in velocity of Earth:

Change in velocity of Earth (Δv) = (m1v1) / m2

Substituting the given values:

Δv = (1.8×10^15 kg × 11 km/s) / 5.98×10^24 kg

B) To determine the average force that Earth exerted on the asteroid while stopping it, we can use the concept of impulse. Impulse is equal to the change in momentum, and the average force can be calculated by dividing the impulse by the stopping time. Here's how to calculate the average force exerted by Earth:

Average force = Impulse / Stopping time

Impulse = Change in momentum = (m1v1)

Stopping time = Distance / Velocity = 0.60 km / 11 km/s

C) To determine the internal energy produced by the collision, we can calculate the kinetic energy of the asteroid before and after the impact, and subtract the initial kinetic energy from the final kinetic energy. Here's how to calculate the internal energy produced by the collision:

Internal energy = Final kinetic energy - Initial kinetic energy

Answer 2

for a)

Step-by-step explanation:

(1.8 x 10^15)(11 x 10^3 m/s) = (5.98 x 10^24 + 1.8 x 10^15)vf

vf= (1.8 x 10^15)(11 x 10^3 m/s) / (5.98 x 10^24 + 1.8 x 10^15)

= 3.3×10−6 m/s