Question

In: Physics

Calculate the maximum acceleration of a car with four wheel drive that is heading up a...

Calculate the maximum acceleration of a car with four wheel drive that is heading up a 8° slope (one that makes an angle of 8° with the horizontal) under the following road conditions. Assume that the static coefficient of friction is involved--that is, the tires are not allowed to slip during the acceleration.

(a) on dry concrete
________m/s2
(b) on wet concrete
_________ m/s2
(c) on ice, assuming that µs = 0.100, the same as for shoes on ice
_________m/s2

Solutions

Expert Solution

coefficient of friction

dry concrete

on wet concrete

on ice

where:
  static friction force.
  Normal force
  car weight
horizontal component of weight


vertical component of the weight

Applying Newton's second law in the x axis

but the sum of the forces on the horizontal axis is equal to

combining equations

remember and

now   

is necessary to obtain expression N

  not accelerate vertically

but also

combining

replacing

  expression of N

substituting in

is obtained

simplifying m

organizing

if

acceleration of gravity

the equation is evaluated for each coefficient of friction

(a) on dry concrete

evaluated numerically

(b) on wet concrete

evaluated numerically

(c) on ice

evaluated numerically

  the negative indicates that the car can not speed upward

genius_generous answered 2 years ago
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