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Centripetal Force and Gravity 4/27/07

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Page 1: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

Centripetal Force and Gravity

4/27/07

Page 2: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

Recap

= sr

= t

= t

s = r

vT = r

aT = r

ac =v2

r

ac = r2

Fc = mac = m v2

r

Fc = mac = mr2

= 2T

Page 3: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

Recap (UCM)Uniform Circular Motion

UCM means that is constantWhich means that… = 0aT = 0|vT| = constant

BUT… vT is not constant because the direction changes

Page 4: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

UCM

Page 5: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

UCM

FSB

Page 6: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

UCM

FSB

Page 7: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

UCM

FSB

FSB

Page 8: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

UCM

FSB

FSB

Page 9: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

UCM

FSB

FSBFSB

Page 10: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

UCM

FSB

FSBFSB

Page 11: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

UCM

FSB

FSBFSB

FSB

Page 12: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

Vertical UCM

Page 13: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

Vertical UCM

FSB

Page 14: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

Vertical UCM

FSB

mg

What’s keeping the ball pinned up against the top?

Page 15: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

Vertical UCM

FSB

mg

What’s keeping the ball pinned up against the top?

Inertia

Page 16: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

Vertical UCM

FSB

mg

Fc = F = FSB + mg

Fc is the sum of the inward forces on the ball.

Fc

Page 17: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

Vertical UCM

FSB

mg

Fc = F = FSB + mg

Fc is the sum of the inward forces on the ball.

Fc

Fc = mr2 = m v2

r

Page 18: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

Vertical UCM

FSB

mg

Fc = F = FSB + mg

Fc is the sum of the inward forces on the ball.

Fc

m = FSB + mg

Fc = mr2 = m v2

r

v2

r

Page 19: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

Vertical UCM

Page 20: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

Vertical UCM

FSB

mg

Fc is the sum of the inward forces on the ball.

Page 21: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

Vertical UCM

FSB

mg

Fc is the sum of the inward forces on the ball.

Fc = F = …

Page 22: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

Vertical UCM

FSB

mg

Fc is the sum of the inward forces on the ball.

Fc = F = FSB

Page 23: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

Vertical UCM

Page 24: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

Vertical UCM

FSB

Page 25: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

Vertical UCM

FSB

mg

Page 26: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

Vertical UCM

FSB

mg

Fc is the sum of the inward forces on the ball.

Fc = F =

Page 27: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

Vertical UCM

FSB

mg

Fc is the sum of the inward forces on the ball.

Fc = F = FSB

Page 28: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

Vertical UCM

FSB

mg

Fc is the sum of the inward forces on the ball.

Fc = F = FSB - mg

Page 29: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

Vertical UCM

FSB

mg

Fc is the sum of the inward forces on the ball.

Fc = F = FSB - mg

Fc = mr2 = m v2

r

m = FSB - mgv2

r

Page 30: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

Vertical UCM

Is the force of the string on the ball greater at the top or at the bottom?

Page 31: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

Vertical UCM

FSB

mg

FSB

mgIs the force of the string on the ball greater at the top or at the bottom?

Page 32: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

Vertical UCM

What is the slowest vT the ball can have if it doesn’t fall when it reaches the top?

Page 33: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

Vertical UCM

What is the slowest vT the ball can have if it doesn’t fall when it reaches the top?

Happens when Fc just counters mg (I.e. FSB = 0)

Page 34: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

Vertical UCM

What is the slowest vT the ball can have if it doesn’t fall when it reaches the top?

m = mgv2

r

Happens when Fc just counters mg (I.e. FSB = 0)

Page 35: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

Vertical UCM

What is the slowest vT the ball can have if it doesn’t fall when it reaches the top?

m = mgv2

r

Happens when Fc just counters mg (I.e. FSB = 0)

= gv2

r

Page 36: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

Vertical UCM

What is the slowest vT the ball can have if it doesn’t fall when it reaches the top?

m = mgv2

r

Happens when Fc just counters mg (I.e. FSB = 0)

= gv2

r v2 = rg

Page 37: Centripetal Force and Gravity 4/27/07. Recap = s r = t = t s = r v T = r a T = r a c = v2v2 r a c = r 2 F c = ma c = m

Vertical UCM

What is the slowest vT the ball can have if it doesn’t fall when it reaches the top?

m = mgv2

r

Happens when Fc just counters mg (I.e. FSB = 0)

= gv2

r v2 = rg

v = rg


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