Physics 12 Newtonian Physics 6 Mr. Jean

The plan: Video clip of the day Circular Motion Demonstrations

Basic Circular Motion question

Chris’ biggest secret is that he’s a stunt car driver. His specialty is the loop. The loop has a radius of 10m and his car has a mass of 1000kg. How fast must he drive his new car to complete the loop successfully? Chris’ driving awesomeness:

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The Loop? Key pieces: –minimum speed to keep this motion –F c = F g When F c = F g the object will continue around the loop without falling away from the circular path. F net = F g + F n = 0 at highest point of the loop.

F g = F c

Solutions:

Basic Circular Motion question

Frictionless Banked Turns: Banked turns create additional centripetal forces. The normal force of a road will provide centripetal forces when it is banked.

Frictionless Banked Turns: Since the car does not move in a vertical direction, the vertical component of the normal force must be equal to the magnitude of gravity. F n cosθ = F g F n cosθ = mg

Frictionless Banked Turns: The horizontal component of the normal force supplies the centripetal force. F n sinθ = F c F n sinθ = (mv 2 ) r

Banked turns:

Frictionless Banked Turns: F net = F c Thus F n sinθ = (mv 2 ) / r F n cos θ mg F n sinθ = (mv 2 ) / r Too messy! Clean up! F n cos θ mg

Frictionless Banked Turns: F net = F c Thus F n sinθ = (mv 2 ) / r F n cos θ mg F n sinθ = (mv 2 ) / r F n cos θ mg

With some simplification we can see that this reduces to something decent. tan θ = v 2 rg This is the maximum speed an object can move around a banked turn without friction.

Example #1: A curve has a radius of 50 meters and a banking angle of 15. What is the critical, speed (the speed for which no friction is required between the car's tires and the surface) for a car on this curve?

Frictionless Banked Turns: Mr. Jean invents a stupid sport for this next year’s Olympics. It is called Rollerblading on ice. The track is circular with a radius of 6 meters. The track has a slope of 25 degrees and the coefficient of friction between the rollerblades and the ice is 0. What is the maximum speed which Olympic competitors will be able to reach (assuming they somehow get to this speed)? What would be the world record lap time?

Lap times What happens if a lap time is slower than _____ seconds? What happens if a lap time is quicker than _____ seconds?

Frictionless Banked Turns: Rollerblading on ice. The track is circular with a radius of 6 meters. The track has a slope of 90 degrees and the coefficient of friction between the rollerblades and the ice is 0.

θ = 90 degrees  AAAAAAAA!!!!!!!! θ = 89.9 degrees  m/s θ = 89 degrees  58.1m/s θ = 75 degrees  14.1m/s θ = 60 degrees  10.1m/s θ = 45 degrees  7.67m/s θ = 30 degrees  5.83m/s θ = 1 degrees  1.01m/s

Questions to work on: P. 559  Grade 12 physics textbook –15, 16, 17, 18 –Solutions will be provided

To do: Read over circular motion. –Pages 551 to 560. Try question #15 page 559, using examples found on pages 555 to 558.

Questions to try: P. 559 –Questions: 16, 17 & 18 P. 556 –Questions: 20, 21 & 22