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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

The total cross-sectional area of the load-bearing calcified portion of the two forearm bones (radius and ulna) is approximately 2.4 cm2. During a car crash, the forearm is slammed against the dashboard. The arm comes to rest from an initial speed of 80 km/h in 5.0 ms. If the arm has an effective mass of 3.0 kg and bone material can withstand a maximum compressional stress of 16 × 107 Pa, is the arm likely to withstand the crash?

To determine
Withstand of arm in the crash.

Explanation

Given info: The arm comes to rest from an initial speed of 80km/h in 5.0ms , the effective mass of arm is 3.0kg , and the cross-sectional area of the load-bearing calcified portion of the two forearm bones is approximately 2.4cm2 .

Explanation: The magnitude of acceleration of the forearm is a=|Δv|/Δt and the force of compression exerted on the arm is F=ma=m(|Δv|/Δt) . Now the compressional stress exerted on the arm is stress=F/A=[m(|Δv|/Δt)]/A by calculating this, we can say whether it can withstand or not.

The formula for the compressional stress in the arm is,

stress=m(|Δv|/Δt)A

m is the effective mass of the arm.

|Δv|/Δt is acceleration of the arm.

A is cross-sectional area of the arm

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