1. General Physics I: Day 9 Equilibrium & Dynamics

2. Sample Problem
Consider a train car being pulled by a locomotive. Draw diagrams for both and consider how they change when the train is at rest, speeding up, cruising at constant speed or slowing down.

3. Splitting Force Pairs
Remember the phrasing: “If object A pushes on object B, then B pushes on A with the same force in the opposite direction.” The two forces that form a force pair always act on different objects! The only thing that determines whether an object accelerates are the forces on that object! (Newton’s 2nd Law)

4. Consider a car at rest. We know that the downward force of gravity on the car and the upward normal force from the road are equal, but why?
Because the two forces form an action/reaction pair.
Because the net force is zero.
Both of the above.
None of the above.

5. Warm-Up: The New Normal
Can the normal force on an object be directed horizontally? If not, why not? If so, provide an example.
~75% → Yes, with a good example
~8% → No!
Can the normal force on an object be directed downward? If not, why not? If so, provide an example.
~50% → Yes, with a good example
~42% → No

6. Warm-Up: The New Normal
Horizontal? “An example would be when a person leans against a wall, the wall pushes back upon them horizontally.” “a) Sure it can. How many times do you want me to run into a wall? It kinda hurts, you know.”

7. Warm-Up: The New Normal
Downward? “I don't think there could be a downward normal force because normal force is acting in the opposite direction of gravitational force. If it's acting downward then it's parallel to the force of gravity and therefore not normal force.” “Yes - balloon on ceiling”

8. In a movie, a tractor trailer collides head on with a motor scooter
In a movie, a tractor trailer collides head on with a motor scooter. During the collision, which object experiences a larger force?
The truck.
The scooter.
Both are the same.
Depends on the speeds involved.
Larger acceleration?

9. Equilibrium
Equilibrium. At rest with zero net force. Comes in two types… stable and unstable

10. A 1.1 kg block is suspended by two cables, each of which is at an angle of θ = 38º with respect to the horizontal. Find the tension T. Round to the nearest single digit answer.
T ~ 1 N
T ~ 3 N
T ~ 6 N
T ~ 7 N
T ~ 9 N

11. Warm-Up: Parachute Forces
A skydiver has a mass of 72 kg and a weight of 706 N. He is descending on a parachute and his speed is still increasing at 1.2 m/s2.
What is the magnitude and direction of the net force on the skydiver?
~50% → 86 N, down
~8% → Down… no magnitude given
~42% → Confusion with magnitude or direction

12. Warm-Up: Parachute Forces
A skydiver has a mass of 72 kg and a weight of 706 N. He is descending on a parachute and his speed is still increasing at 1.2 m/s2.
What is the magnitude and direction of the force that the parachute harness exerts on the skydiver?
~25% → 620 N, up
~8% → Up… no magnitude given
~58% → Confusion with one or both

13. Warm-Up: Parachute Forces
“A. Using newtons second law, the sum of forces is equal to mass times acceleration, I can use the given information about these quantities and plug them into my equation. Using Newton's second law I find that the net force on the skydiver is 86.4[N] and going straight down.”

14. Warm-Up: Parachute Forces
“a. The net force has a magnitude and direction of N downwards, because the skydiver still has an acceleration og 1.2 m/s^2 and that multiplied by his mass of 72 kg = 86.4N 8.The parachute exerts N on the skydiver in the upward direction. We know that the net force is the sum of the two other forces and for this reason to subtract 706 from to find the force of the parachute on the skydiver.”

15. Connecting Forces & Acceleration
Dynamics: Objects experiencing a net force.
Steps:
Prep-work: FBD, convert units, break up vectors
Apply Newton’s 2nd Law on each axis
Solve mathematically
Combine or interpret results

16. Worked-Example: Block on Incline
30°
50 kg
Determine the block’s acceleration down the ramp.

17. Worked-Example: Block on Incline
1. Explain why tilting the coordinate system simplified the problem. Think about how the procedure would have changed had traditional x- y coordinates been used.

18. Worked-Example: Block on Incline

19. Worked-Example: Block on Incline
Lining up your axes with the acceleration will (almost) always make the math easier. It doesn’t change the physics at all… just how hard you have to work in solving it.

20. Coming up…
Thursday (9/18) → 5.3 – 5.4 Tuesday (9/23) → 5.5 & Catch-up (no WarmUp) Thursday (9/25) → Review for Exam 1 Tuesday (9/30) → Exam 1 Warm-Up due Wednesday by 10:00 PM Homework #4 due today by 11:59 PM Homework #5 due Saturday the 27th The Mini-Exam…

21. Mini-Exam
Average: 33/55, 60% (middle D on my scale) This was intended to give feedback and let you know what the exams will be like. This is worth 5% of your total grade. Come talk! Don’t like your score? me! You will get a generic explaining “The Deal”. Read it carefully. The offer expires when we have Exam 1.