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# Inquiry: NASCAR

## Purpose: To determine critical velocity equation around a track with friction.

In this experiment we will be using a rotating platform. The object of the first part of this experiment is to derive the equation for critical velocity that a car can travel around a flat track without sliding off. You will remember that the force needed to hold a mass in a circular path is: For objects on a rotating disk, friction provides the centripetal force. On a frictionless disk there would be no centripetal force. As you can see from the above equation, the centripetal force is proportional to v2 and inversely proportional to the radius.

## Part 1 Procedure for Un-banked Turn:

• Draw the FBD and derive the equation for velocity.

• Launch Data Studio, select Smart Pulley Rotational, enter 30 degrees as the spoke angle and under setup choose only rotational velocity. Using the mass provided, loop the string over the center of the table so the mass won't fly completely off the table. In your first trial use a radius of 0.20 m and determine the critical velocity from the computer. Use this to determine μ.

• Now use a radius of 0.30 m and μ to predict a critical velocity. Perform the experiment and calculate a % error. The computer will give you angular velocity in rad/s so don't forget to multiply it by the radius to get the actual linear velocity.

• Determine the coefficient of friction (μ) between the car and the wood for later use in NASCAR Part 3. (radius = 0.23 m)

## Part 2 Procedure for Banked Turn (no friction):

• Draw the FBD and derive the equation for velocity.

• When an automobile goes around a curve on a level road (see last question), friction between the tires and the road is required to provide the necessary force to keep the car on the road. If the road is coated with ice, the frictional force may be too small to provide necessary force and the car will slide off the road. If the road is suitably banked, the car will go around the curve without requiring any frictional force.

• Draw an FBD and derive an equation in your notebook for critical velocity of an object on a banked turn with no friction.

• We will be using the ball so that the friction will be negligible. Choose the angle of the incline, give the disk a push to rotate at a speed that will roll the ball up the incline, and then let the disk coast and record the angular velocity when the ball will roll down the incline. Predict the critical velocities at various angles of inclination (10º, 20º and 30º). (radius = 0.32 meters)

## Part 3 Procedure for Banked Turn (friction):

In the real world we need to deal with friction. This time in our drawings we will use a car traveling around a banked curve and we will ask the question, "When will the car slide UP the incline?"

Draw the FBD in your notebook and derive the maximum and minimum critical velocity equations for an object traveling around a banked curve when there is friction present.  Place the car on the incline. Slowly increase the rotation of the disk until the car activates the switch and the buzzer sounds. Record the angular velocity so that you can determine the linear velocity. Also use the maximum equation above to calculate what the velocity should be. Change the angle of incline (10.0º, 15.0º, 20.0º) and record the velocity in your notebook. The radius is 0.23 m and we previously calculated μ in Part 1.

Safety Factors: Banked turns can be labeled with safety factors. The maximum safety factor would equal the maximum critical velocity divided by the posted speed limit. The minimum safety factor would equal the posted speed limit divided by the minimum critical velocity.

## Inquiry Questions:

1. What is the smallest radius in which you can turn a car if you are moving 65.0 mph and the coefficient of friction between the tires and the road is 0.330? (1 mph is 0.447 m/s)

2. Use the following for questions 2-3:
1 mph = .447 m/sec
μ dry pavement = 0.900
μ wet pavement = 0.650
μ snow packed = 0.300

3. A road has a tight turn with a radius of 40.0 meters. The bank is 32.0 degrees and the road is snow packed.

• What is the maximum velocity in mph you can drive and stay on the road?

• If the safety factor is 1.60, what speed limit is posted in mph?

• What is the lowest velocity in mph that you can exit without sliding down?

4. An off-ramp has a speed limit of 45.0 mph and a radius of 70.0 meters.

• If the pavement is dry and NOT banked, what is the safety factor?

• If the pavement is wet, what bank angle would allow the car to maintain the same maximum velocity?