Vehicle in Circular Motion#

Part 1#

A car of mass 2100.0 \(\rm{kg}\) in uniform circular motion accelerates towards the _________ of the circle due to the force of __________ friction between the car’s tires and the road. Please fill in the blanks with one of the options below (The choices are presented in the same order as they should appear in the sentence.)

Fig. 1 The left side of the image is a diagram labelled 'Top view of vehicle in uniform circular motion' with a circle below. There is a top view of a vehicle on the leftmost point on the circle (180 degrees from the 0 position) with the y axis extending upwards from the vehicle, and the x axis extending similarly towards the right. The right side of the image is titled 'Rear view of vehicle in uniform circular motion' and contains two axes, z (upwards) and x (rightwards) which cross perpendicularly to form a four quadrant graph. At the origin of this graph is a rear-view symbol of the vehicle.

Answer Section#

  • centre, kinetic

  • outside, static

  • centre, static

  • outside, kinetic

Part 2#

If the car moves at 94.0 \(\rm{km/h}\) around a circle of radius 99.0 \(\rm{m}\), find the acceleration of the car in SI units.

Answer Section#

Please enter in a numeric value.

Part 3#

Draw a free body diagram in the \(xz\) plane (the plane shown on the right of Fig.1) to show the forces acting on the car in the directions perpendicular to the car’s motion. Please upload a pdf titled “fbd1”.

Answer Section#

File upload box will be shown here.

Part 4#

Find the size of the frictional force that keeps the car in circular motion.

Answer Section#

Please enter in a numeric value.

Part 5#

Above what speed would the car’s frictional force be overcome as the car tries to follow this curve?

\(\mu_s =\) , \(\mu_k =\) , \(\mu_r =\)

Answer Section#

Please enter in a numeric value.

Part 6#

If the curve was banked toward the centre of the circle at an angle of 20.0\(^{\circ}\) as shown on the right of Fig. 2, draw a free body diagram for the forces acting on the car in the directions perpendicular to the direction of motion as the car moves around the circle at 94.0 \(\rm{km/h}\).

Please upload a pdf titled “fbd2”.

Fig. 2 The left side of the image is a diagram labelled 'Top view of vehicle in uniform circular motion' with a circle below. There is a top view of a vehicle on the leftmost point on the circle (180 degrees from the 0 position) with the y axis extending upwards from the vehicle, and the x axis extending similarly towards the right. The right side of the image is titled 'Rear view of vehicle in uniform circular motion' and contains two axes, z (upwards) and x (rightwards) which cross perpendicularly to form a four quadrant graph. At the origin of this graph is a rear-view symbol of a vehicle, angled downwards below the positive x-axis at an angle labelled as theta.

Answer Section#

File upload box will be shown here.

Part 7#

Resolving your vectors, solve for the force of friction required to keep the car in uniform circular motion at this speed with the banked curve.

Answer Section#

Please enter in a numeric value.

Attribution#

Problem is licensed under the CC-BY-NC-SA 4.0 license.
The Creative Commons 4.0 license requiring attribution-BY, non-commercial-NC, and share-alike-SA license.