EF 151– Physics for Engineers
Fall, 2016
Lab 4-3: Forces and Circular Motion
Objectives
- Become proficient at solving forces for circular motion in a vertical plane
- Derive equations for banked turns with friction
- Use resources to estimate the coefficient of friction between car tires and the road
Task 1. Tennis ball on a string
A 1/8 pound tennis ball is tied to a string and twirled in a 1.5 ft radius circle. Start by drawing a FBD=KD for each
part of the problem.
a. Determine the minimum angular velocity (in rpm) so the string remains taut through the entire circle.
Check your solution by trying it.
b. For the angular velocity in part a, determine the maximum tension in the string.
c.
For the angular velocity in part a, determine the tension in the string when the tennis ball is at 30° below
the horizontal.
EF 151– Physics for Engineers
Fall, 2016
Task 2. Car on a banked turn
How can we determine the bank angle needed for a car going at 60 mph on a track with a 200 ft radius? Let’s
break it down into some manageable steps to see how we can come to a solution.
A good representation of a car on a banked turn is shown below. (http://plaza.obu.edu/corneliusk/up1/bc_f.pdf).
Using the coordinate system shown (horizontal and vertical) write out Newton’s second law in each direction.
Substitute and solve for the Normal Force from the y component.
Substitute the expression for the Normal force into the x component equation and solve for θ. Hint: multiply by
(1/cosθ)/(1/cosθ) and remember what sinθ/cosθ equals.
Do some quick internet research to estimate the coefficient of friction between a car tire and the road under dry
conditions. You must have at least three sources.
Determine the minimum required bank angle for a speed of 60 mph and a curve radius of 200 ft. Also determine
the minimum required bank angle for a speed of 60 mph and a curve radius of 500 ft.
Fill out the required form for this lab.