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acceleration involving centripetal motion?
A 1600 kg car starts from rest and drives around a flat 64-m-diameter circular track. The forward force provided by the car's drive wheels is a constant 1200 N.
1)What is the magnitude of the car's acceleration at t=13s
2)What is the direction of the car's acceleration at t=13s ? Give the direction as an angle from the r-axis.....theta=?
3)If the car has rubber tires and the track is concrete, at what time does the car begin to slide out of the circle. t=?
There are two accelerations to consider in this problem:
Tangential Accel (at) and Centripetal Accel (ac)
Here is the tangential acceleration
Force provided by car = F = m at
m is the mass of car. This acceleration will be constant as the force is also constant. You can go ahead and calculate that.
The linear velocity of the car, at a given time, is calculated as
v = at t
You can calculate at from the eq above and t is given in the problem. Please note that this velocity will change over time.
The centripetal acceleration is given by
ac = omega^2 x radius
ac = (v)^2 / radius
where the circular motion equations were used. Note that the centripetal acceleration will change over time.
The total acceleration, in magnitude, is
a = sqrt (ac^2 + at^2)
as you know, the acceleration is a vector and the two components are given by tangential and centripetal components of it, which are always orthogonal. This answers 1)
2) the car has traveled a distance d along a circle given by
d = at t^2 2
from regular cinematic equations. You already calculated at and t is given. That d corresponds to a portion of the circumference of a circle so the total angular distance is
ang distance = 360 degrees * d / (pi*D)
where pi=3.14 and D is the diameter given in the problem. This answers 2)
To solve 3), you need to know that the maximum frictional force has to be equal to the centripetal force so
Fr = fric-coeff * mass of car * gravity = mass of car * ac
fric-coeff is the one that corresponds to rubber over concrete and the mass of the car is given. With this equation, find the value of ac and, remember that I mentioned that the centripetal acceleration changes over time? find the equation above and calculate the time. This should answer 3).
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