Question

Sort the following quantities into categories of "known," "to find," or "unneeded." Let m and v be the mass and speed of the car, respectively; μs​ is the coefficient of static friction, r is the radius of the circular path, n is the magnitude of the normal force acting on the car, and ΣFx​ is the x-component of the net force acting on the car.

Answer 1

The known values include the car's mass, speed, and the circular path's radius. To find values depend on the problem but typically involve the coefficient of static friction, the normal force, and the net force. Mass is sometimes an unneeded quantity as it can cancel out in equations.

Step-by-step explanation:

To answer the student's question, we must sort the given quantities into the appropriate categories. The known values are the mass (m) and speed (v) of the car, and the radius (r) of the circular path since these are given. The to find values will differ depending on the specific problem being solved but could include the coefficient of static friction (μs), the normal force (n), and the x-component of the net force acting on the car (ΣFx). μs is especially important as it directly affects the frictional force that allows the car to negotiate curves. The unneeded quantities cannot be determined without the context of the problem but they usually include any variable not directly involved in the equations being used to solve the problem.

In the scenario described, the equation Fc = mv²/r or Fc = mrω² (where ω is the angular velocity) could be used to find the centripetal force (Fc). The fact that mass cancels out indicates that the mass of the car is not a crucial factor in these calculations, so m can be considered an unneeded value in the context of comparing vehicles of different masses negotiating a turn, as long as the equation is used correctly.