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 new location, is the meter stick still balanced? How would you balance it again?

2. Compare torque and net force. 4/31/07 Lesson #69 Topic: Torque Objectives: (After this class I will be able to) 1. Define torque. 2. Compare torque and net force. 3. Calculate the net torque acting on an object. Warm Up: ? Assignment:

Torque Net force causes linear acceleration. Net torque causes rotational acceleration. Rotational acceleration: speed up or slow down rate of rotation (a change in rotation). Torque is the rotational analog of force Torque is caused by a force exerted on a lever. Examples: A wrench, a see-saw, a door, ect…

Torque example Consider trying to balance a .1kg meter stick on the 40cm mark. The meter stick will not balance. It will begin to rotate. It rotates because the weight of the meter stick causes a net torque. The force acts at the CG (50cm mark) Fw 40cm

Net Torque 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 a 100g meter stick that is hung from the 20cm mark? 0.3 N m 3 N m 30 N m 3000 N m 0 of 20

Zero Net Torque If an object is not rotating, or is rotating at constant speed, the net torque = zero. This means that there is no torque acting on it, or that the clockwise torque equals the counterclockwise torque. Example#1: A meter stick is hung from the 50cm mark. An additional 2kg is hung from the 80cm mark. What mass must be hung from the 10cm mark for the system to balance?

Example 1

Lesson #70 Topic: Lab:Torque 4/30/07 Lesson #70 Topic: Lab:Torque Objectives: (After this class I will be able to) Use the concept of net torque to solve for the mass of a meter stick. 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!)

Project Describe how a door works. Why is it designed the way it is? Why is the door knob located at the end of the door? Why not the middle?

Lesson #71 Topic: Cross product and Net Torque 4/31/07 Lesson #71 Topic: Cross product and Net Torque Objectives: (After this class I will be able to) 1. Compare torque and work. 2. Describe the difference between “cross” and “dot” products. 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 3.75 N m 0 N m 0 of 5

Torque vs. Work Torque is similar to work Both are found by multiplying a force by a distance. However, there are special requirements. Remember: W= F ∙ d this is a “dot” product. This dot product means that F and d must be parallel. If not parallel, then you have to use the component of the force that is parallel to the distance moved.

Work

Torque vs. Work Torque is found using a “cross” product. Cross product means that the force and the radius have to be perpendicular to one another. If not perpendicular to one another, then use the component of the force that is perpendicular. r = radius of rotation.

Torque r Fx PP θ Fy F

Torque Example Door looked at from above. r=1.5m hinge Knob θ= angle between F and r = 90° F=20N

Torque Example Door looked at from above. r=1.5m hinge θ= angle between F and r = 0° F=20N

Torque Example Door looked at from above. r=1.5m hinge θ= 30° θ= angle between F and r = 30° F=20N

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

Example Find the net torque θ= 31° F2=25N PP θ= 23° θ= 45° 2m 4m

A meter stick is balanced at the 8 cm mark and a 1kg mass is hung from the 0 end of the meter stick. What is the mass of the meter stick? 0kg 0.19N 1.9kg 190g 0 of 5

You have a 0. 234m long wrench. A job requires a torque of 32 You have a 0.234m long wrench. A job requires a torque of 32.4N m, and you exert a force of 232N. What is the smallest angle between the force and the lever at which the force can be exerted? 0.597° 36.6° 53.4° 90° 0 of 5

You stand on the petal of a bicycle You stand on the petal of a bicycle. If you have a mass of 65kg, the petal makes an angle of 35° above the horizontal, and the petal is 18cm from the center of the chain ring. How much torque do you exert? 117N m 95.8N m 67.1N m 6.71N m 0 of 5

Kariann (56kg) and Aysha (43kg) want to balance on a 1 Kariann (56kg) and Aysha (43kg) want to balance on a 1.75 m long seesaw. Where should they place the pivot point? 0.99m from Aysha 1.3m from Aysha 0.76m from Aysha 0.88m from Aysha 0 of 5

1cm mark 10cm mark 15cm mark 35cm mark A 0.1kg meter stick is hung from the 25cm mark. A 0.2kg mass is hung from the 45cm mark. Where must a 0.65kg mass be hung so the system balances? 1cm mark 10cm mark 15cm mark 35cm mark 0 of 5

Bonus A ladder of length 2m and mass 1kg is leaning against the wall such that the ladder makes an angle of 60° with respect to the floor. With what horizontal force must I exert on the bottom of the ladder to prevent it from slipping and falling? Assume no friction between the ladder and the floor or wall. 2m F=? 60°