Project ► Balance a meter stick. ► Now add weight to one side of the meter stick and adjust it so that it is still balanced. ► Now move the weight to a

ProjectProject

►Balance a meter stick. Balance a meter stick. ►Now add weight to one side of the Now add weight to one side of the

meter stick and adjust it so that it is meter stick and adjust it so that it is still balanced.still balanced.

►Now move the weight to a new Now move the weight to a new location, is the meter stick still location, is the meter stick still balanced?balanced?

►How would you balance it again?How would you balance it again?

Lesson #69Lesson #69Topic: TorqueTopic: TorqueObjectives: Objectives: (After this class I will be able to)(After this class I will be able to)

1. Define torque.1. Define torque.

2. Compare torque and net force.2. Compare torque and net force.

3. Calculate the net torque acting on an 3. Calculate the net torque acting on an object.object.

4/31/07

Warm Up: ?

Assignment:

TorqueTorque► Net force causes linear acceleration. Net force causes linear acceleration. ► Net torque causes Net torque causes rotational accelerationrotational acceleration..► Rotational accelerationRotational acceleration: speed up or slow : speed up or slow

down rate of rotation (a change in rotation). down rate of rotation (a change in rotation). ► Torque is the rotational analog of Torque is the rotational analog of

forceforce► Torque is caused by a Torque is caused by a forceforce exerted on a exerted on a

leverlever..

Examples: A wrench, a see-saw, a door, ect… Examples: A wrench, a see-saw, a door, ect…

Torque exampleTorque example

►Consider trying to balance a .1kg Consider trying to balance a .1kg meter stick on the 40cm mark.meter stick on the 40cm mark.

►The meter stick will not balance. It will The meter stick will not balance. It will begin to rotate.begin to rotate.

► It rotates because the weight of the It rotates because the weight of the meter stick causes a meter stick causes a net torquenet torque..

►The force acts at the CG (50cm mark)The force acts at the CG (50cm mark)

Fw40cm

Net TorqueNet Torque

rFnetnet

nnet ...21

rF•The torque acting on the meter stick would be the weight of the meter stick times the distance to the pivot point.

What is the net torque acting on What is the net torque acting on a 100g meter stick that is hung a 100g meter stick that is hung

from the 20cm mark?from the 20cm mark?

0 of 20 0.3

N m

3 N

m

30

N m

300

0 N m

0% 0%0%0%

1.1. 0.3 N m0.3 N m

2.2. 3 N m3 N m

3.3. 30 N m30 N m

4.4. 3000 N m3000 N m

Zero Net TorqueZero Net Torque

► If an object is not rotating, or is rotating If an object is not rotating, or is rotating at constant speed, the net torque = at constant speed, the net torque = zero.zero.

►This means that there is no torque This means that there is no torque acting on it, or that the clockwise torque acting on it, or that the clockwise torque equals the counterclockwise torque.equals the counterclockwise torque.

►Example#1: A meter stick is hung from Example#1: A meter stick is hung from the 50cm mark. An additional 2kg is the 50cm mark. An additional 2kg is hung from the 80cm mark. What mass hung from the 80cm mark. What mass must be hung from the 10cm mark for must be hung from the 10cm mark for the system to balance?the system to balance?

Example 1Example 1

Lesson #70Lesson #70Topic: Lab:TorqueTopic: Lab:TorqueObjectives: Objectives: (After this class I will be able to)(After this class I will be able to)

1.1. Use the concept of net torque to solve Use the concept of net torque to solve for the mass of a meter stick.for the mass of a meter stick.

4/30/07

Lab Task #1: Create an experiment to solve for the mass of your meter stick.

Lab Task #2: Create an experiment that will solve for the mass of an unknown object.Assignment: Lab Report due at the end of the

period

(show all calculations!)

ProjectProject►Describe how a door works. Describe how a door works. ►Why is it designed the way it is? Why is it designed the way it is? ►Why is the door knob located at the Why is the door knob located at the

end of the door? Why not the middle? end of the door? Why not the middle?

Lesson #71Lesson #71Topic: Cross product and Net Torque Topic: Cross product and Net Torque Objectives: Objectives: (After this class I will be able to)(After this class I will be able to)

1. Compare torque and work.1. Compare torque and work.

2. Describe the difference between 2. Describe the difference between “cross” and “dot” products.“cross” and “dot” products.

4/31/07

Warm Up: What is the torque on a bolt produced by a 15N force exerted perpendicular to a wrench that is 25cm long?

Assignment: Torque Practice

What is the torque on a bolt produced by a 15N force exerted perpendicular to a wrench

that is 25cm long?

375

N m

37.

5 N m

3.7

5 N m

0 N

m

25% 25%25%25%1.1. 375 N m375 N m

2.2. 37.5 N m37.5 N m

3.3. 3.75 N m3.75 N m

4.4. 0 N m0 N m

0 of 5

Torque vs. WorkTorque vs. Work► Torque is similar to work Torque is similar to work ► Both are found by multiplying a force by a Both are found by multiplying a force by a

distance.distance.► However, there are special requirements.However, there are special requirements.► Remember: W= F ∙ d this is a “dot” product.Remember: W= F ∙ d this is a “dot” product.► This dot product means that F and d must be This dot product means that F and d must be

parallelparallel..► If not parallel, then you have to use the If not parallel, then you have to use the

component of the force that is parallel to the component of the force that is parallel to the distance moved.distance moved.

cosFddFW

WorkWork

Torque vs. WorkTorque vs. Work► Torque is found using a “cross” product.Torque is found using a “cross” product.► Cross product means that the force and the Cross product means that the force and the

radius have to be radius have to be perpendicularperpendicular to one to one another.another.

► If not perpendicular to one another, then If not perpendicular to one another, then use the component of the force that is use the component of the force that is perpendicular.perpendicular.

► r = radius of rotation.r = radius of rotation.

sinFrrF

TorqueTorque

PP

r

Fx

Fy

θ

F

Torque ExampleTorque Example►Door looked at from above.Door looked at from above.

r=1.5m

F=20N

Knob hinge

θ= angle between F and r = 90°


r=1.5m

F=20N

hinge



r=1.5m

F=20N

hinge


θ= 30°

ExampleExample► A bolt on a car engine needs to be tightened A bolt on a car engine needs to be tightened

with a torque of 35N m. You use a 25cm with a torque of 35N m. You use a 25cm long wrench and pull on the end of the long wrench and pull on the end of the wrench at an angle of 60° from the wrench at an angle of 60° from the perpendicular. How much force do you have perpendicular. How much force do you have to exert?to exert?

ExampleExample►Find the net torqueFind the net torque

PP

F1=30N

θ= 45° θ= 23°

θ= 31° F2=25N

F3=10N

4m

2m

A meter stick is balanced at the 8 cm mark A meter stick is balanced at the 8 cm mark and a 1kg mass is hung from the 0 end of the and a 1kg mass is hung from the 0 end of the meter stick. What is the mass of the meter meter stick. What is the mass of the meter

stick?stick?

0 of 5 0

kg

0.1

9N

1.9

kg

190

g

25% 25%25%25%1.1. 0kg0kg

2.2. 0.19N0.19N

3.3. 1.9kg1.9kg

4.4. 190g190g

You have a 0.234m long wrench. A job You have a 0.234m long wrench. A job requires a torque of 32.4N m, and you exert a requires a torque of 32.4N m, and you exert a

force of 232N. What is the smallest angle force of 232N. What is the smallest angle between the force and the lever at which the between the force and the lever at which the

force can be exerted?force can be exerted?25% 25%25%25%

1.1. 0.597°0.597°

2.2. 36.6°36.6°

3.3. 53.4°53.4°

4.4. 90°90°

0 of 5

You stand on the petal of a bicycle. If you You stand on the petal of a bicycle. If you have a mass of 65kg, the petal makes an have a mass of 65kg, the petal makes an angle of 35° above the horizontal, and the angle of 35° above the horizontal, and the petal is 18cm from the center of the chain petal is 18cm from the center of the chain

ring. How much torque do you exert?ring. How much torque do you exert?

117

N m

95.

8N m

67.

1N m

6.7

1N m

25% 25%25%25%1.1. 117N m117N m

2.2. 95.8N m95.8N m

3.3. 67.1N m67.1N m

4.4. 6.71N m6.71N m

0 of 5

Kariann (56kg) and Aysha (43kg) want Kariann (56kg) and Aysha (43kg) want to balance on a 1.75 m long seesaw. to balance on a 1.75 m long seesaw. Where should they place the pivot Where should they place the pivot

point?point?

0.9

9m fr

om A

ysha

1.3

m fr

om A

ysha

0.7

6m fr

om A

ysha

0.8

8m fr

om A

ysha

25% 25%25%25%

1.1. 0.99m from 0.99m from AyshaAysha




0 of 5

A 0.1kg meter stick is hung from the 25cm A 0.1kg meter stick is hung from the 25cm mark. A 0.2kg mass is hung from the 45cm mark. A 0.2kg mass is hung from the 45cm

mark. Where must a 0.65kg mass be hung so mark. Where must a 0.65kg mass be hung so the system balances?the system balances?

0 of 5

25% 25%25%25%

1.1. 1cm mark1cm mark




BonusBonus► A ladder of length 2m and mass 1kg is A ladder of length 2m and mass 1kg is

leaning against the wall such that the ladder leaning against the wall such that the ladder makes an angle of 60° with respect to the makes an angle of 60° with respect to the floor. With what horizontal force must I exert floor. With what horizontal force must I exert on the bottom of the ladder to prevent it on the bottom of the ladder to prevent it from slipping and falling? Assume no friction from slipping and falling? Assume no friction between the ladder and the floor or wall.between the ladder and the floor or wall.

2m

60°F=?

Documents

Project ► Balance a meter stick. ► Now add weight to one side of the meter stick and adjust it so that it is still balanced. ► Now move the weight to a