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# Answer to Question #128584 in Mechanics | Relativity for Amelia

Question #128584
A race car collided with race track wall.Just before the collision,he is travelling at speed v1= 70m/s along a straight line at 30 degrees from the wall. Just after collision he is travelling at speed 50m/s along a straight line at 10 degree from the wall.His mass is 80kg.(a) the impulse J of the driver due to collision
(b)the collision last for 14ms.What is the magnitude of the average force on the driver during collision
1
2020-08-06T16:46:30-0400

The change of impulse can be calculated as the sum of changes in parallel and perpendicular to the wall directions.

"J_{\\text{par}} = m(v_2\\cos\\alpha_2 - v_1\\cos\\alpha_1) = 80\\,\\mathrm{kg}\\cdot(50\\,\\mathrm{m\/s}\\cdot\\cos10^\\circ - 70\\,\\mathrm{m\/s}\\cdot\\cos30^\\circ ) = -911\\,\\mathrm{kg\\cdot m\/s} \\\\\nJ_{\\text{perp}} = m(v_2\\sin\\alpha_2+ v_1\\sin\\alpha_1) = 80\\,\\mathrm{kg}\\cdot(50\\,\\mathrm{m\/s}\\cdot\\sin10^\\circ+ 70\\,\\mathrm{m\/s}\\cdot\\sin30^\\circ ) =3495\\,\\mathrm{kg\\cdot m\/s}."

(a) The total change of impulse of the driver can be calculated by means of the Pythagorean theorem:

"J = \\sqrt{J_{\\mathrm{par}}^2 + J_{\\mathrm{perp}}^2} = 3611\\,\\mathrm{kg\\cdot m\/s}."

(b) The change of impulse obtained above is due to the force from interaction with the wall. So the average force can be calculated as

"F_{\\text{av}} = \\dfrac{J}{\\Delta t} = \\dfrac{3611\\,\\mathrm{kg\\cdot m\/s}}{0.014\\,\\mathrm{s}} \\approx 2.6\\cdot10^5\\,\\mathrm{N}."

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