Stuck on physics h.w. A 7 kg car travels in a flat circle. At a certain instant the velocity of the car is?

Question

24 m/s west & the total acceleration of the car is 7 m/s^2 at 56 degrees north of west.

What is its radius? Answer in units of km.

Answer 1

The key concepts of this question are alluded to with the phrase, "flat circle", this indicates it is a circular motion problem which we must utilize our knowledge centripetal force.

Two things to remember about circular motion,
-velocity is always tangent to the path
-centripetal acceleration is always perpendicular to the velocity and is pointed inward to along the radius of the circle.

First we must resolve the acceleration given to us in the problem into its X and Y components since this is not a 'uniform' circular motion problem apparently, the car is both acceleration centripetally AND tangentially.
It helps to draw out a diagram of the situation to help visual what is happening.
To find the upward component of the acceleration, multiply the given value by the sine of 56 degrees, giving us an upward (centripetal) acceleration of 5.8 m/s^2.

We are given the instantaneous velocity of the car.

Plug into the formula,
centripetal acceleration = v^2 / R
the upward acceleration we just calculate is the centripetal acceleration since it points inward towards the center of the path, normal to the tangential acceleration which pointed along the path.
5.8 m/s^2 = (24 m/s)^2 / R
R = (24 m/s)^2 / 5.8 m/s^2
R = 99.25 m
R = .09925 km

It turns out that the mass of the car is irrelevant to solve this problem.


EDIT:
"need help!", I did use the angle of acceleration, I just wrote it out in words and not explicitly in a mathematical statement.
I said, in words, this,
Upward acceleration = 7 m/s^2 * sin (56 degrees) = 5.8 m/s^2

One needs to use the sine of the angle to get the normal component of the acceleration; the cosine will give the component of acceleration which is parallel to the velocity (angular acceleration). "need help!", what you found, this is not the centripetal acceleration.

Answer 2

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