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Specific Forces

Centripetal Force

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Warm up

• Planet Zonk is twice as far from the sun as Earth. What is its period?

• Herman the astronaut ( mass 80kg) is floating in orbit about earth and feels a gravitational attraction of 360 newtons. What is the value of gravity at his location?

• What is his orbital radius as a multiple of earth’s radius.

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Objectives

· Explain why a body moving with uniform circular motion must be regarded as undergoing  acceleration and state the direction of the acceleration.

· Predict the path of an object which has a force acting on it perpendicular to the direction of its velocity.

· Indicate the direction of the instantaneous velocity, centripetal acceleration, and centripetal force for an object moving at constant velocity in a circle.

· Calculate centripetal acceleration and force.

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Imagine…Imagine…• Think about the moon on its journey around

the earth…• How about an amusement park ride that

spins you around in a constant circle…• How do you describe this kind of circular

motion?• Is the velocity constant or is it accelerating?• How does the moon stay up there in the

sky?

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What Is Uniform Circular Motion?

• Uniform Circular Motion is motion in a circle with: – Constant Radius R

– Constant Speed v = |vv|

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What if the String Breaks?

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Centripetal Force

• Provides acceleration toward the center which causes an object to continually change velocity because it is changing direction while the speed remains constant.

Fc = mac

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What happens when you turn.

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Without Centripetal Force

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With Centripetal Force

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Force is Perpendicular to the Velocity

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Check your understanding

An object is moving in a clockwise direction around a circle at constant speed. Use your understanding of the concepts of velocity, acceleration, and force to answer the next five questions. Use the diagram shown at the right.

A

B

C

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Vector 1

1. Which vector below represents the direction of the force vector when the object is located at point A on the circle?

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Vector 2

• 2. Which vector below represents the direction of the force vector when the object is located at point C on the circle? 

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Vector 3

• Which vector below represents the direction of the velocity vector when the object is located at point B on the circle?

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Vector 4

• 4. Which vector below represents the direction of the velocity vector when the object is located at point C on the circle?

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Vector 5

• 5. Which vector below represents the direction of the acceleration vector when the object is located at point B on the circle?

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Motion in a circle

• Velocity is a vector; it has direction• An object travelling in a circle at constant speed is

continuously changing direction• Therefore, it is accelerating• Thus, requires a force

r

2v

a

rmmF

2v

a

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Centripetal Acceleration

• This acceleration can be calculated

ac = v2 / r

a is the centripetal acceleration

v is the speed

r is the radius of the circle

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Circular Speed

• As speed is distance traveled divided by the time it takes to travel the distance

v = 2r/Tv is the speed

r is the radius of the circle

T is the period of revolution

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Practice 1

A runner moving at a speed of 8.8 m/s rounds a bend with a radius of 25 m.

What is the centripetal acceleration of the runner?

3.1 m/s2

What provided this acceleration to the runner?

friction between his shoes and the track

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Practice 2

Racing on a flat track, a car going 32 m/s rounds a curve 56 m in radius.

What is the car’s centripetal acceleration?18 m/s2

What would be the minimum coefficient of static friction between tires and road that would be needed for the car to round the curve without skidding?

1.8

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Homework

• A/c # 6 and 7

• Problems 13 to 20