A car of mass m is negotiating a circular turn of radius R and speed v on a banked road with an angle of banking θ. The forces on the car are shown below. Ignore friction in this problem. Draw a free body of the car.Identify and show the radial direction. Pick coordinate axes with x pointing in the radial direction towards the center of the circle and y in the vertical direction. Show the coordinate axes on the free body diagram.Set up Newton’s Laws in the radial and vertical direction. Which force provides the centripetal force?Use the equations in part C to solve for the speed of the car in terms of R, Does the speed depend on the mass of the car?If R=250.0 m, m=750.0 kg, calculate the speed of the car. This image illustrates a car on an inclined plane and the forces acting upon it. There are several components and forces depicted:1. **Car on Incline**: The car is positioned on a slope, which is shown at an angle \( \theta \).2. **Forces**: - **Weight (\( w \))**: Represented by a downward arrow, indicating the force of gravity acting on the car. - **Normal Force (\( N \))**: Shown as an arrow perpendicular to the inclined surface indicating the support force exerted by the surface on the car. - **Vertical and Horizontal Components**: The vertical axis is denoted as "Vertical," and the axis perpendicular to it, along the inclined plane, is labeled "Horizontal."3. **Reference Angles**: - \( \theta \): The angle between the inclined track and the horizontal plane.The diagram is useful for understanding the effect of an inclined plane on an object, focusing on gravitational and normal forces, and how these forces decompose into components parallel and perpendicular to the incline.

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A car of mass m is negotiating a circular turn of radius R and speed v on a banked road with an angle of banking θ. The forces on the car are shown below. Ignore friction in this problem. Draw a free body of the car.

A car of mass m is negotiating a circular turn of radius R and speed v on a banked road with an angle of banking θ. The forces on the car are shown below. Ignore friction in this problem. Draw a free body of the car.

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