A car rounds a banked curve as shown in the figure below. The radius of curvatur

Question

A car rounds a banked curve as shown in the figure below. The radius of curvature of the road is R, the banking angle is ?, and the coefficient of static friction is ?s.

(a) Determine the range of speeds the car can have without slipping up or down the road. (Use any variable or symbol stated above along with the following as necessary: g.)
vmin =
vmax =

(b) Find the minimum value for ?s such that the minimum speed is zero. (Use any variable or symbol stated above along with the following as necessary: g.)
?s =

Explanation / Answer

(a) Look at the forces that affect the slide. They are parallel to the direction of the road surface. These are 1) The component of car weight along the surface, pulling the car down the bank; 2) the component of centrifugal force along the surface, pulling the car up the bank 3) the frictional force acting in the direction of the weaker force and equal to µ times the sum of the normal components of weight and centrifugal force. The three forces are then 1) Fcp = m*v²/R*cos? 2) Fgp = m*g*sin? 3) µ*(m*v²/R*sin? + m*g*cos?) The car will slip up the surface if 1) exceeds the sum of 2) and 3) this defines vmax: m*vmax²/R*cos? = m*g*sin? + µ*(m*vmax²/R*sin? + m*g*cos?) solve for vmax and you will get your answer. The car will slip down the surface if 2) exceeds the sum of 1) and 3), this defines vmin: m*g*sin? = m*vmin²/R*cos? + µ*(m*vmin²/R*sin? + m*g*cos?) solve for vmin (b) with v = 0, only gravity affects the car, so only forces 2) and 3) are involved. However, 3) is now µ*m*g*cos?. For the car not to slip, 3) must be = 2): µ*m*g*cos? = m*g*sin?; µ = tan? (c) use the results from (a) with those values.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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