Force Exerted by Road on an Accelerating Car

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SUMMARY

The discussion centers on calculating the force exerted by the road on a 2300 kg SUV accelerating from 0 to 60 mph in 9 seconds. The acceleration is determined to be 2.98 m/s², leading to a horizontal force (Fx) of 6854.61 N using the formula F=ma. The vertical force (Fy) due to gravity is calculated as 22540 N. The total force exerted by the road is derived from the vector sum of these forces, confirming that the correct calculation involves using the Pythagorean theorem, resulting in a force of approximately 24600 N.

PREREQUISITES
  • Understanding of Newton's Second Law (F=ma)
  • Basic knowledge of vector addition
  • Familiarity with gravitational force calculations
  • Ability to convert units (e.g., mph to m/s)
NEXT STEPS
  • Study vector addition in physics to understand force components
  • Learn about gravitational force calculations in different contexts
  • Explore unit conversion techniques, especially for speed
  • Investigate real-world applications of Newton's laws in automotive physics
USEFUL FOR

Students in physics, automotive engineers, and anyone interested in the dynamics of vehicle motion and force calculations.

yoshi824
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Homework Statement



A huge SUV of mass 2300 kg can accelerate from 0 to 60 mi/h in 9.0 s. What force does the road exert on the SUV?

V0 = 0
V= 60mph or 26.8224m/s
M= 2300kg
t=9s

Homework Equations



F=ma

The Attempt at a Solution


a= (26.8224) / 9 = 2.98
Fx = ma = 2.98*2300 = 6854.61 N

Fy = m*g = 2300*9.8 = 22540 N

So those are the two forces that I was able to calculate but I am not sure how I find the force exerted by the road on the car. Any help would be greatly appreciated! Thanks!

other info: I read somewhere that the force would be sqrt (Fx2 + Fy2) but that didn't give me the right answer if my above work is correct.
 
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If you made a mistake I would like to know what it is. Your work looks right to me.
 

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