Ch. 12 - Static Equilibrium; Elasticity and Fracture

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179당신이 사용하는 게 아니라요?교과서 변경

Giancoli Douglas 5th edition

Ch. 12 - Static Equilibrium; Elasticity and Fracture

문제 95e

12장, 문제 95e

Suppose a 65-kg person jumps from a height of 3.0 m down to the ground. Estimate the stress and determine if the tibia will break in a stiff-legged landing (d = 1.0 cm).

검증된 단계별 안내

Determine the force exerted on the tibia during the landing. Start by calculating the velocity just before impact using the equation for free fall:

\sqrt{2 g h}

, where g is the acceleration due to gravity (9.8 m/s²) and h is the height (3.0 m).

Estimate the deceleration during the landing. Assume the stopping distance (compression of the tibia) is approximately equal to the diameter of the tibia,

d = 1.0 cm = 0.01 m

. Use the kinematic equation

v^{2} = 2 a d

to solve for the deceleration

a

Calculate the force exerted on the tibia using Newton's second law:

F = m a

, where

m

is the mass of the person (65 kg) and

a

is the deceleration calculated in the previous step.

Determine the stress on the tibia. Stress is defined as force per unit area:

σ = F / A

. The cross-sectional area of the tibia can be approximated as a circle with diameter

d = 1.0 cm

, so

A = π(d /2)

².

Compare the calculated stress to the breaking stress of the tibia (approximately 1.6 × 10⁸ N/m²). If the calculated stress exceeds this value, the tibia will break; otherwise, it will not.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Potential Energy

Potential energy is the energy stored in an object due to its position in a gravitational field. For a person jumping from a height, this energy can be calculated using the formula PE = mgh, where m is mass, g is the acceleration due to gravity, and h is the height. As the person falls, this potential energy is converted into kinetic energy, which is crucial for understanding the forces involved upon landing.

Impact Force

Impact force is the force exerted by an object when it comes to a sudden stop after falling. It can be estimated using the impulse-momentum theorem, which relates the change in momentum to the force applied over the time of impact. In a stiff-legged landing, the impact force is concentrated over a short distance, leading to higher stress on the bones, which is essential for assessing the risk of injury.

Stress and Strain

Stress is defined as the force applied per unit area within materials, while strain is the deformation that occurs as a result of that stress. In the context of the tibia during a landing, calculating the stress involves determining the impact force and the cross-sectional area of the bone. Understanding these concepts helps in evaluating whether the stress exceeds the bone's strength, which could lead to a fracture.

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