PM (10%) Problem 6: Calculate the maximum acceleration of a car that is heading

Question

PM (10%) Problem 6: Calculate the maximum acceleration of a car that is heading up a 7.5° slope (one that makes an angle of 7.5° with the horizontal and assuming up the slope is the positive direction) under the following road conditions. Assume that the car has four-wheel drive and that the coefficient of static friction is involved that is, the tires are not allowed to slip during the acceleration System Static friction Kinetic friction 1.0 0.7 0.6 005 0.9 0.1 0.4 0.7 0.5 0.3 0,03 07 0.05 0.02 Rubber on dry concrete Rubber on wet concrete Steel on steel(dry) Steel on steel (oiled) Shoes on wood Shoes on ice Steel on ice Randomized Variables Ctheexpertta.com OR 33% Part (a) Calculate the maximum acceleration of the car on dry concrete in m 33% Part (b) Calculate the maximum acceleration of the car on wet concrete in m s2 . s st 33% Part (c) Calculate the maximum acceleration of the car on ice in m s-, assuming that , =100. the same as for shoes on ice. 9022 Grade Summary Deductions Potential 100% cos0 Submissions Attempts remaining: cotan0 asin acos per attempt) atano acotano sino cosh tanh0 cotano Degrees Radians detailed vie END O BACKSPACECLEAR Submit Hist t give up Hintdeduction per bint Husts renng Feedback:s deduction per feedback

Explanation / Answer

Solution:-

Component of weight down hill = mgsin()
Component of weight normal to road F = mgcos()

uphill force is the 'grip' between road and tires. Its maximum value is the maximum static frictional force, just before wheels spin and car loses its grip.

This force = F = mgcos()

At the point where wheels are about to lose grip, the maximum resultant uphill force, F, is:
F = mgcos() - mgsin()

Using F = ma gives:
mgcos() - mgsin() = ma
g(cos() - sin()) = a

Using the above formula to find 'a' for each of the conditions.

a = g(cos() - sin())
. .= 9.81(1.0cos(7.5°) - sin(7.5°))
. .= 8.46m/s²

b)a = g(cos() - sin())
. .= 9.81(0.7cos(7.5°) - sin(7.5°))
. .= 5.53m/s²

c) a = g(cos() - sin())
. .= 9.81(0.1cos(7.5°) - sin(7.5°))
. .= -0.31m/s²

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.