On September 8, 2004, the Genesis spacecraft crashed in the Utah desert because its parachute did not open. The 210210210-kg capsule hit the ground at 311311311 km/h and penetrated the soil to a depth of 81.081.081.0 cm. 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.

Ch 05: Applying Newton's Laws

Young & Freedman Calc - University Physics 14th Edition

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Young & Freedman Calc 14th Edition

Ch 05: Applying Newton's Laws

Problem 13b

Chapter 5, Problem 13b

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 $311$ km/h and penetrated the soil to a depth of $81.0$ cm. 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.

Verified step by step guidance

Step 1: Convert the velocity of the capsule from km/h to m/s. Use the conversion factor: 1 km/h = 0.27778 m/s. Multiply 311 km/h by this factor to express the velocity in m/s.

Step 2: Calculate the deceleration (negative acceleration) experienced by the capsule during the crash. Use the kinematic equation:

v^{2} = u^{2} + 2 a s

, where

v

is the final velocity (0 m/s),

u

is the initial velocity (converted in Step 1),

a

is the acceleration, and

s

is the penetration depth (81.0 cm converted to meters). Rearrange the equation to solve for

a

a = - u^{2} / (2 s)

Step 3: Calculate the net force exerted on the capsule using Newton's second law:

F = m a

, where

m

is the mass of the capsule (210 kg) and

a

is the deceleration calculated in Step 2.

Step 4: Calculate the weight of the capsule using the formula:

W = m g

, where

g

is the acceleration due to gravity (approximately 9.8 m/s²).

Step 5: Express the force exerted by the ground as a multiple of the capsule's weight. Divide the force calculated in Step 3 by the weight calculated in Step 4:

F / W

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Force and Newton's Second Law

Force is defined as any interaction that, when unopposed, will change the motion of an object. According to Newton's Second Law, the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). In this scenario, the force exerted by the ground on the capsule can be calculated by determining the deceleration of the capsule as it comes to a stop upon impact.

Weight and Gravitational Force

Weight is the force exerted on an object due to gravity and is calculated as the product of the object's mass and the acceleration due to gravity (W = mg). For the Genesis capsule, its weight can be determined using its mass (210 kg) and the standard gravitational acceleration (approximately 9.81 m/s²). This value serves as a reference point for comparing the force exerted by the ground during the crash.

Impulse and Momentum

Impulse is the change in momentum of an object when a force is applied over a period of time. It is equal to the product of the average force and the time duration over which the force acts. In the context of the capsule's crash, the impulse experienced by the capsule can be used to determine the average force exerted by the ground, as it relates to the change in the capsule's velocity from its impact speed to zero.

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Textbook Question

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 $311$ km/h and penetrated the soil to a depth of $81.0$ cm. What was its acceleration (in m/s² and in g's), assumed to be constant, during the crash?

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Three sleds are being pulled horizontally on frictionless horizontal ice using horizontal ropes (Fig. E $5.14$ ). The pull is of magnitude $190$ N. Find the tension in ropes $A$ and $B$ .

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