1. Angled Work
Physics

2. Trigonometry
Here are some diagrams to help you with the trigonometry. Try to figure it out yourselves before you ask for help.

3. Generating pressure under cart.
Trigonometry
Good so call it: G
Bad so call it: B
Generating pressure under cart. F

4. Now Complete the:
Angled Work Lab

5. Trigonometry Cos θ = G F Cos θ = A H Sin θ = O H USEFUL Force =
USELESS Force =
Cos θ = G F
Sin θ = B F
F Cos θ
F Sin θ

6. Modified work Equation:
W = F d Cos θ

7. Practice
Bob is pushes a large crate 15 meters across the floor with 250 Newtons of force. He is so tall that he has to bend over to push at a 65 degree angle. Draw a picture.
1. Draw a vector diagram to show the direction of the push and the direction that the crate moves. Remember to start both of the arrows at the point (0,0).

8. 2. How much of the pushing force was USEFUL?
3. How much of the pushing force was NOT useful?
4. How much work did Bob do?
5. How much work could Bob have done if he had pushed the box straight forward instead of at an angle? Why do you think humans don’t usually push this way?

9. Practice
Betty pulls her brother 45 meters in a wagon with 175 N of force. The handle makes an angle of 50 degrees. Draw a picture.
1. Draw a vector diagram to show the direction of the pull and the direction the wagon moved. Remember to start both of the arrows at the point (0,0).

10. 2. How much of the pulling force was USEFUL?
3. How much of the pulling force was NOT useful?
4. How much work did Betty do?
5. How much work could Betty have done if she had pulled the wagon straight forward instead of at an angle? Why do you think humans don’t design wagons to work this way?

11. Practice
Let’s try a harder one. Bob is vacuuming his house. He pushes on the vacuum handle with 110 N of force at a downward angle of 35 degrees. He cleans 22 meters of carpet. Meanwhile, friction resists with a force of 55 N. Draw a picture.

12. 1. How much work did Bob do? (Draw vector picture.)
2. How much work did friction do? (Draw vector picture.)
3. How much work was done total?

13. Review Question
Bob is pulling his sister 38 meters in a sled with 140 N of force. Her mass is 32 kg. The rope makes a 42 degree angle. The coefficient of friction between the sled and the snow is Draw a picture.
1. What is the normal force between the sled and the snow? (Draw force diagram.)

14. 2. How strong is the force of friction?
3. How much work did Bob do? (Draw vector diagram.)
4. How much work did friction do? (Draw vector diagram.)
5. What was the total work done?