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:

The Loop?

• Key pieces:– minimum speed to keep this motion

– Fc = Fg

• When Fc = Fg the object will continue around the loop without falling away from the circular path.

• Fnet = Fg + Fn = 0 at highest point of the loop.

• Fg = Fc

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.

Fncosθ = Fg

Fncosθ = mg

Frictionless Banked Turns:

• The horizontal component of the normal force supplies the centripetal force.

Fnsinθ = Fc

Fnsinθ = (mv2)

r

Banked turns:

Frictionless Banked Turns:

• Fnet = Fc

• Thus

Fnsinθ = (mv2) / r

Fn cos θ mg

Fnsinθ = (mv2) / r Too messy! Clean up!

Fn cos θ mg

Frictionless Banked Turns:

• Fnet = Fc

• Thus

Fnsinθ = (mv2) / r

Fn cos θ mg

Fnsinθ = (mv2) / r

Fn cos θ mg

• With some simplification we can see that this reduces to something decent.

tan θ = v2

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 183.64m/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