Genesis Crash. On September 8,2004, the Genesis spacecraft...

Genesis Crash. On September $8,2004,$ the Genesis spacecraft crashed in the Utah desert because its parachute did not open. The 210 -kg capsule hit the ground at 311 $\mathrm{km} / \mathrm{h}$ and penetrated the soil to a depth of 81.0 $\mathrm{cm}$ . (a) Assuming it to be constant, what was its acceleration (in $\mathrm{m} / \mathrm{s}^{2}$ and in $g^{\prime} \mathrm{s} )$ during the crash? \right. (b) What force did the ground exert on the capsule during the crash? Express the force in newtons and as a multiple of the capsule's weight. (c) For how long did this force last?

Genesis Crash. On September $8,2004,$ the Genesis spacecraft crashed in the Utah desert because its parachute did not open. The 210 -kg capsule hit the ground at 311 $\mathrm{km} / \mathrm{h}$ and penetrated the soil to a depth of 81.0 $\mathrm{cm}$ .
(a) Assuming it to be constant, what was its acceleration (in $\mathrm{m} / \mathrm{s}^{2}$ and in $g^{\prime} \mathrm{s} )$ during the crash? \right.
(b) What force did the ground exert on the capsule during the crash? Express the force in newtons and as a multiple of the capsule's weight. (c) For how long did this force last?

Key Concepts

Constant Acceleration

This concept assumes that the acceleration (or deceleration) remains the same throughout the impact or crash. It simplifies the problem by allowing constant values to be used in kinematic equations, which is a common approach in collision analysis.

Kinematic Equations

Kinematic equations relate displacement, velocity, acceleration, and time when acceleration is constant. These equations, such as the relation v² = u² + 2ad, are fundamental tools for analyzing motions, including deceleration during crashes.

Newton's Second Law

Newton's Second Law, expressed as F = ma, connects the mass of an object and its acceleration to the applied net force. This principle is crucial for determining forces during impacts and understanding how changes in motion result from applied forces.

Unit Conversion

Accurate unit conversion is critical in physics problems to ensure that all quantities are compatible. Converting units, for example from kilometers per hour to meters per second, is necessary to correctly apply kinematic equations and compute accelerations and forces.

Impulse and Time Calculation

This concept involves analyzing the duration over which a force is applied to change an object's momentum. By relating the acceleration (or deceleration) to the change in velocity, one can estimate the time interval of the impact, which is important for understanding the effects of forces during collisions.

Transcript

00:01 Welcome to this tutorial.

00:04 Part a is essentially asking what the acceleration of the capsule is in relationship to the gravitational acceleration or gravity.

00:18 So if we start with part a, you must first select the correct equation based on newton's second law of motion and kinematic.

00:40 Formulation.

00:48 This particular equation, we can find that information out by solving for a.

00:58 So first, we must convert the 30011 kilometers per hour velocity component into meters per second.

01:22 The distance the capsule moves into the earth after impact is 81 centimeters or 0 .81 meters.

01:37 It started from some original velocity of zero.

01:42 So we cancel that out.

01:49 So now we can solve for a.

02:03 And we square 86 .4 meters per second.

02:08 We get 74, 65 meters squared, second squared.

02:15 Then two times the depth of impression.

02:21 0 .81 meters is 1 .62 meters.

02:29 That leaves us with, a collision acceleration of 4 ,608 meters per second squared, then divided into gravitational acceleration.

02:49 We have approximately 470 times gravitational acceleration are 470 gs, which equates to 4 ,608 meters per second squared, collision acceleration.

03:17 So part a is asking what is the acceleration in meters per second squared and in gs during the crash? and the answer to part a is 470 gs or 4 ,608 meters per second squared.

03:49 To solve part b, we must calculate the multiples of force the crash exerted on the capsule by finding the summation of newton's second law of motion, force is equal to mass times acceleration...

Please give Ace some feedback