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A force of 48N acts on a particle on a rough horizontal plane and at an angle of 20° above the horizontal. Given the particle is on the point of slipping, the coefficient of friction between the particle and the plane is 0.6, what is the mass of the particle? Ans: 9.35 kg Hint: the particle is not moving. How does this apply to FF and FAX?

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Vertical Forces A

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What holds elevators up? A rope or a cable These are associated with the “response force” called Tension F T You can think of F T as the opposing force to the F W and therefore is equal but opposite to F W if velocity is constant.

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The Elevator Question "You are standing on a bathroom scale in an elevator. You are holding an apple. (Yes, people are staring at you...) You weigh 500 Newtons, so your mass is about 50 kg.“ In this problem we will round the force of gravity to 10m/s 2

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Elevator Is At Rest What does the scale read? If you let go of the apple, what does it do?

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Elevator Is At Rest What does the scale read? 500N If you let go of the apple, what does it do? Free Fall (acceleration towards earth at ~10m/s 2 )

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The Elevator Accelerates Upward at 2m/s 2 What does the scale read? If you let go of the apple, what does it do?

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The Elevator Accelerates Upward at 2m/s 2 What does the scale read? 600N If you let go of the apple, what does it do? It accelerates (free fall) downward at 2m/s m/s 2 = 12m/s 2

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The Elevator Moves Up With Constant Velocity at 10m/s What does the scale read? If you let go of the apple, what does it do?

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The Elevator Moves Up With Constant Velocity at 10m/s What does the scale read? 500 N If you let go of the apple, what does it do? Falls like when elevator at rest at ~10m/s 2

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The Elevator Slows Down (While Going Up) at 2m/s 2 downward What does the scale read? 400N If you let go of the apple, what does it do? The apple appears to fall slower (10m/s 2 -2m/s 2 = 8m/s 2 ) Think of this in the same way as accelerating downward!

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The Elevator Speeds Up (While Going Down) at 2m/s 2 downward What does the scale read? If you let go of the apple, what does it do? The results are the same as when you were slowing down at top. Only concerned about direction of the acceleration

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The Elevator Moves Down With Constant Velocity at 10m/s What does the scale read? If you let go of the apple, what does it do?

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Elevator Is At Rest What does the scale read? If you let go of the apple, what does it do?

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A 2000 g mass accelerates upward at 1.2 m/s 2. What is the upward force? 2000g 1.2 m/s 2 F NET = 2.4N F W = 19.6 N F T = F NET + F W F T = 22 N

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What is happening the object below? How would you determine acceleration? 250 N 100 N It is accelerating upward with a net force of 150 N Find the mass using F W (100N). Then insert into F = ma m= 10.2 kg a = (150 N) / (10.2kg) a = 14.7 m/s 2 upward

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VERTICAL FORCES

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How do we use Tension F T when looking at hanging objects? FTFT FWFW

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As the elevator car accelerates up, a force is exerted __________________ which more than counters the downward force of _________________. Thus, the car experiences a net upward force. upward gravity

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As the elevator car accelerates down, the ______________________ force of gravity is antagonized by the tension in the rope (a force acting _________________). downward upward

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When the car is stationary (or ____________), the upward force ______________ the downward force. static equals

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Which force is larger when an elevator accelerates upwards? FTFT FWFW F NET = F T - F W (going up)

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Which force is larger when an elevator accelerates downwards? FTFT FWFW F NET = F W - F T (going down)

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A 15 kg crate is being pulled up using a rope. Find the tension on the rope under the following circumstances: If the crate accelerates upward what is greater, F T or F W ? F T If crate accelerates downward what is greater, F T or F W ? F W The crate moves upward with a constant velocity what is greater, F T or F W ? No unbalanced force; F T = F W The crate moves downward with a constant velocity what is greater, F T or F W ? No unbalanced force; F T = F W

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A 15 kg crate is being pulled up using a rope. Find the tension on the rope under the following circumstances: The crate accelerates upward at 6.58m/s 2 ? What is F NET ? F NET = m a (Use the acceleration of the object upward) (15 kg) (6.58m/s 2 ) = 98.7N What Forces make up F NET ? F W and F T Calculate F W F W = (15 kg) (9.8m/s 2 ) = 147N Now calculate F T If going up: F NET = F T – F W F T = F NET + F W F T =246N

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A 15 kg crate is being pulled up using a rope. Find the tension on the rope under the following circumstances: The crate accelerates downward at 6.58m/s 2 ? What is F NET ? F NET = m a (Use the acceleration of the object upward) (15 kg) (6.58m/s 2 ) = 98.7N What Forces make up F NET ? F W and F T Calculate F W F W = (15 kg) (9.8m/s 2 ) = 147N Now calculate F T If going down: F NET = F W – F T F T = F W - F NET F T = 48.3 N

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Millenium Force Go to You tube 308 ft 4.5 “g” 92 mph

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NEW! Official Millennium Force POV - YouTubeNEW! Official Millennium Force POV - YouTube zwHg

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On a rollercoaster When do you feel weightless? When do you feel heaviest? WHY???????? Since you asked……

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