A 1070-kg car and a 2250-kg pickup truck approach a curve on the expressway that

Question

A 1070-kg car and a 2250-kg pickup truck approach a curve on the expressway that has a radius of 205m .

A) At what angle should the highway engineer bank this curve so that vehicles traveling at 65.3mi/h can safely round it regardless of the condition of their tires?

B) Should the heavy truck go slower than the lighter car?

C) As the car and truck round the curve at 65.3mi/h , find the normal force on the car to the highway surface.

D) As the car and truck round the curve at 65.3mi/h , find the normal force on the truck to the highway surface

Explanation / Answer

A) angle of banking,

theta = tan^-1(v^2/(g*R))

here, v is maximum speed

R ---> radius of curve

g ---> acceleration due to gravity

v = 65.3 mi/h

= 65.3*1.609 kmh

= 65.3*1.609*5/18 m/s

= 29.18 m/s

so,

theta = tan^-1(29.18^2/(9.8*205))

= 23 degrees

b) No.

angle of Banking does not depend on mass of Vehicle.

c)
N = m1*g*cos(theta)

= 1070*9.8*cos(23)

= 9654 N

d)
N = m2*g*cos(theta)

= 2250*9.8*cos(23)

= 20300 N

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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