General Physics I: Day 8 Weight & Newton’s 3rd Law

Difficult/Interesting “I would really like to go over the fbds some more, id like to know exactly which forces are necessary to be drawn on the diagram.”

Sample FBD A block rests in the corner of two angled planks. Draw a FBD for the block that accurately reflects the relative strengths of each force. Can we see this both graphically and with components? 1 2

Warm-Up: Hitting the Wall 2.0 Suppose you run into a wall at 4.5 m/s (~10 mph). The time it takes for you to go from moving to not moving is very short. Estimate your acceleration and then calculate the force (in newtons) that the wall exerted on you during the stopping. ~25% → Time (Δt) was too long. (0.5 sec or more) ~25% → Reasonable force est. → 1,700 – 4,500 N ~8% → Calculation or units errors ~42% → Confused or stuck Range of force estimates: 0 N – 8,800 N

Warm-Up: Hitting the Wall 2.0 “It takes a short amount of time to go from moving to stopping so if it takes 1 second to stop moving then the acceleration would be 4.5m/s^2. Then I convert my weight from pounds to kg which would be 54.4kg so the equation to find force (in N) would be 4.5m/s^2*54.4kg=244.8N. Since the wall will exert the same amount of force as the force I will exert on the wall, the amount of force exerted on me during the stopping will be - 244.8N.”

Warm-Up: Hitting the Wall 2.0 “If you are walking 4.5m/s and quickly stop which takes about 0.2 seconds we can estimate that the acceleration is 22.5m/s^2. Say our mass is 77 kg(170 lbs) The force the wall exerted on me would be my acceleration times the mass which is about 1700 N.”

Newton’s 2nd Law The net force on an object is equal to the mass of that object times it’s acceleration. This is one way to define mass: Mass is how resistant something is to changes in motion (acceleration). Vector equation! Be careful adding forces…

Using Newton’s 2nd Law Newton’s 2nd Law is not a definition of force! It relates forces on an object to the object’s motion When using the equation, we fill in each side of the equation separately: In more than 1D, split this into separate equations.

Worked-Example: Dogsled How much is the force that the dog team exerts on the sled train, 𝐹 𝑑 ? What is the magnitude of the force that the cargo sled exerts on the passenger sled, 𝐹 𝑐𝑝 ? Free-Body Diagrams (FBDs)

Worked-Example: Dogsled 1. What is the net force on the passenger sled? ~30% ~20% (errors) ~50%

Worked-Example: Dogsled 2. How much force is needed to accelerate the passenger sled at a rate of 2.3 m/s^2? Justify your answer.

Worked-Example: Dogsled Explain in your own words why the answer to the previous two questions came out to be the same force. ~20% → Didn’t get the same for 1 & 2 ~40% → Because of special circumstances (const. 𝑎 , sleds connected, no friction, etc.) ~20% → Newton’s 3rd laws causes cancellation ~20% → It has to due to Newton’s 2nd law

Worked-Example: Dogsled

Warm-Up: Block vs. Hand In Case 1, Block B accelerates Block A across a frictionless table. In Case 2, a force of 98 N accelerates Block A across the same table. The acceleration of Block A in Case 2 is ~2% → zero. ~27% → greater than in Case 1. ~7% → less than in Case 1. ~64% → the same as in Case 1.

Warm-Up: Block vs. Hand Best plan: Treat the two blocks as one being pulled by a force of 98 N Another good view: Look at B… how hard will it pull on the rope?

Weight – The Force of Gravity Weight ( 𝐹 𝑔 or 𝑤 ) is the force of gravity and is different than an object’s mass. Recall: A force is an interaction that would cause acceleration if it were unopposed How fast do you accelerate if gravity is the only force acting on you? Downward at 9.8 m/s2 of course! On the surface of planet Earth, we can always use this to calculate or weight.

Difficult/Interesting “What I found the most interesting about the reading was how people still don't really know how to talk about mass or weight. If it weren't for a taking this course, a lot of us wouldn't know how to differentiate between the too.” Student question about weight vs. mass

Difficult/Interesting “Im still confused about how or when to use mass or weight. In the reading it says that both weight and mass can be the same thing but have distinctions. The way I see mass and weight is that weight is how heavy something is, and mass is how big an object is. Is that how they are distinguished or am I not fully understanding the difference between weight and mass.” Student question about weight vs. mass

Consider a person standing in a rocket that is accelerating upward Consider a person standing in a rocket that is accelerating upward. The upward force exerted by the rocket floor on the person is larger than equal to smaller than the downward force of gravity on the person.

Now suppose the rocket is moving upward at constant velocity Now suppose the rocket is moving upward at constant velocity. The upward force exerted by the rocket floor on the person is larger than equal to smaller than the downward force of gravity on the person.

(short) Sample Problem Two children fight over a 200 g stuffed bear. The 25 kg boy pulls to the right with a 15 N force and the 20 kg girl pulls to the left with a 17 N force. Ignore all other forces on the bear. At this instant… What can you say about the velocity of the bear? What can you say about the acceleration of the bear?

Forces As Interactions So far, we have proposed two ways of defining a force: A push or a pull. (informal/intuitive) An interaction that causes acceleration. (formal) A force is also an “interaction” between two objects. For every force, you should be able to identify: What object is it applied to? What object is causing the force? Is it a contact or long distance force?

The Law of Force Pairs From Newton: “To every action [force] there is always opposed an equal reaction; or, the mutual actions of two bodies are always equal, and directed to contrary parts.” Every interaction affects both objects If the interaction gets stronger, both objects are affected more. Thus, all forces come in pairs with the two forces having equal strength and opposite direction.

Reaction Forces Use this phrasing to help your understanding: “If object A pushes on object B, then B pushes on A with the same force in the opposite direction.” We literally switch the two objects to describe the reaction force. Very helpful in confusing action-reaction situations.

Warm-Up: Pushing the Wall “Wondering if the "choose this option to get full credit" was a trick...” Nope… that would be a mistake. (or… a trick on myself?)

Warm-Up: Pushing the Wall You push on a solid concrete wall which doesn't move. Is your push the only horizontal force on the wall? ~5% → Yes, because of Newton's 1st Law ~14% → Yes, because of Newton's 2nd Law ~28% → No, because of Newton's 2nd Law ~55% → No, because of Newton's 3rd Law

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.

Coming up… Tuesday (9/16) → 5.1 – 5.2 Thursday (9/18) → 5.3 – 5.4 Tuesday (9/23) → 5.5 (no WarmUp) Thursday (9/25) → Review for Exam 1 Tuesday (9/30) → Exam 1 Warm-Up due Monday by 10:00 PM Homework #4 due Tuesday the 16th Homework #5 due Saturday the 27th