Physics 211Lecture 5

Today’s Concepts:a) Free Body Diagramsb) Force due to stringsc) Force due to springsd) Force due to gravity

Classical Mechanics

F mar r

Free Body Diagrams1)Choose system (object or group)2)Draw forces acting on object

-action at a distance - Gravity-contact - things touching

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Free Body Diagrams

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Free Body DiagramsFree Body Diagrams

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Free Body DiagramsFree Body Diagrams

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Free Body DiagramsFree Body Diagrams

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Always, always, always Always, always, always startstart with a free body diagram. with a free body diagram.Do Do notnot write any equations before you have drawn write any equations before you have drawnall the forces in a free body diagram!all the forces in a free body diagram!

Tension ForceDirection: Parallel to rope, always pulling.Magnitude: As much or little as needed for Fnet=ma

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m2

m1

g

Demo: 2 skateboards+ rope

Checkpoint

A box of mass m is hung with a string from the ceiling of an elevator that is accelerating upward. Which of the following best describes the tension T in the string:

A) T < mg B) T = mg C) T > mg

a

I drew a FBD and then I wrote down the equation for newton's law. Using this I determined that T=mg+ma

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BOX IN THE ELEVATOR!!! OMG

Tension ACT

A block weighing 4 lbs is hung from a rope attached to a scale. The scale is then attached to a wall and reads 4 lbs. What will the scale read when it is instead attached to another block weighing 4 lbs?

A) 0 lbs. B) 4 lbs. C) 8 lbs.

m m m

?

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Normal Force

"It is what it has to be to do what it does" !!??"It is what it has to be to do what it does" !!??

Normal force is the force perpendicular to the surface that prevents the objects from passing through each other.1)Direction: Perpendicular to surface and out2)Magnitude: As much or little required keep objects separate.

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Checkpoint

A block sits at rest on a horizontal frictionless surface. Which of the following sketches most closely resembles the correct free body diagram for all forces acting on the block? Each arrow represents a force.

There are only two forces acting on the box. Gravity is the arrow pointing down and the normal force is the upward arrow.

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ACT

A block accelerates down a frictionless inclined plane. Which of the following sketches most closely resembles the correct free body diagram for all forces acting on the block? Each arrow represents a force.

A B C D

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Spring ForceDirection: Parallel to spring: Push or pullMagnitude:F=-kx

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Demo: Hooke’sLaw blackboard

Springs ExampleI would like to have more examples with the spring force. PLEASE!

A 5 kg mass is suspended from a spring with spring constant 25 N/m.How far is the spring stretched from its equilibrium position?

A) 0.5 m B) 2 m C) 5 m

F ma0k x Mg

Mgxk

5*9.825

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Checkpoint

A box of mass m is hung by a spring from the ceiling of an elevator. When the elevator is at rest the length of the spring is L = 1 m. If the elevator accelerates upward the length of the spring will be:

A) L = 1 mB) L < 1 mC) L > 1 m

m

aL

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ACT

You are traveling on an elevator up the Sears tower. As you near the top floor and are slowing down, your acceleration

A) is upwardB) is downwardC) is zero

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VV

ACT

You are traveling on an elevator up the Sears tower, and you are standing on a bathroom scale.

As you near the top floor and are slowing down, the scale reads

A) More than your usual weightB) Less than your usual weightC) Your usual weight

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ACT

A cart with mass m2 is connected to a mass m1 using a string that passes over a frictionless pulley, as shown below. The cart is held motionless (a = 0).

The tension in the string isA) m1gB) m2gC) 0

m2

m1

g

a = 0

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ACT

A cart with mass m2 is connected to a mass m1 using a string that passes over a frictionless pulley, as shown below. Initially, the cart is held motionless, but is then released and starts to accelerate.

After the cart is released, the tension in the string is

A) = m1gB) > m1gC) < m1g

m2

m1

g

a

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Universal Gravitation

Could we talk a little bit more about the Newton gravitational force formula and its relation with g? 2

MmF Gr

2earth

earth

M mF G

R

Near surface of earth r=Rearth

3 224

1126

5.97 106.67 10

6.4 10/

kgm kg s

mm

29.8 /m s m

Direction: Toward other object (down near earth surface)Magnitude:F=GMm/r2 (mg near earth surface)

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General Comments

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The spring example, if the elevator is accelerating upwards, The spring example, if the elevator is accelerating upwards, then the box is accelerating downwards? so the force of then the box is accelerating downwards? so the force of what causes the box to go downwards?what causes the box to go downwards?

Explain tension in a spring, and whether the length of the Explain tension in a spring, and whether the length of the spring increases or decreases based upon tension. It makes spring increases or decreases based upon tension. It makes sense when real world scenarios are considered, but what is sense when real world scenarios are considered, but what is the scientific explanation of it?the scientific explanation of it?

Tension please especially the whole elevator thing.Tension please especially the whole elevator thing.

Nothing too intense.Nothing too intense.