A car is driven on a large revolving platform which rotates with constant angula

Question

A car is driven on a large revolving platform which rotates with constant angular speed . At t = 0 a driver leaves the origin and follows a line painted radially outward on the platform with constant speed v0. The total weight of the car is W, and the coefficient of friction between the car and stage is .

(a) Find the acceleration of the car as a function of time using polar coordinates. Draw a clear vector diagram showing the components of acceleration at some time t > 0.

(b) Find the time at which the car just starts to skid.

(c) Find the direction of the friction force with respect to the instantaneous position vector r just before the car starts to skid. Show your result on a clear diagram

Explanation / Answer

In the given problem

a) In polar coordinates,

acceleration of car is a = ( ¨ r r ) ^ r + ( r¨ + 2r) ^

a=(r¨r)r^+(r¨+2r)^

Here, r¨=0, =, ¨=0 and r=v0. Substituting,

a = r^r + 2v0 ^

Hence the acceleration is  a = r^r + 2v0 ^

b) Time (t)

To calculate the time friction force=centrifugal force.

W = r2
At time t, r = v0t Solving for t

t = W/ v02

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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