Question

(11%) Problem 4: A 82.5-kg person is riding in a car moving at 20.5 m/s (assume this is the positive direction) when the car runs into a bridge abutment. This problem will illustrate why the invention of the airbag dramatically improved the safety of automobiles. 50% Part (a) Calculate the horizontal component of the average force, in newtons, on the person if he is stopped by a padded dashboard that compresses an average of 1.25 cm. Grade Summary Fdash Deductions Potential 100% 0 ( A E sino cos) tan cotan asin) acos atano acotan sinho Cosh) Bình) có anh) Degrees Radians Submissions Attempts remaining: 5 (O per attempt detailed view VONESENCE Subenit I give up! Hints: 09 deduction per hint. Hints remaining: 2 Feedback: deduction per feedback 50% Part (b) Calculate the horizontal component of the average force, in newtons, on the person if he is stopped by an air bag that compresses an average of 165 cm Allan 2020 per TA, LLC

Answer 1

Given :

Mass (m) = 82.5 kg

Initial speed (u) = 20.5 m/s

Final speed (v) = 0 m/s

Part (a) Solution :

Here, d = 1.25 cm = 0.0125 m

Using equation : v² - u² = 2ad

Thus : a = ( v² - u² ) / 2d = - (20.5)² / 2(0.0125) = - 16180 m/s²

thus : Force = ma = (82.5)(- 16180) = - 1386825 N

Part (b) Solution :

Here, d = 16.5 cm = 0.165 m

So: a = - (20.5)² / 2(0.165) = - 1273.485 m/s²

thus : Force = m a = (82.5)(- 1273.485) = - 105062.5 N