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Lecture 2, Newton’s Laws Phys 100, How Things Work
Newton’s laws
What’s a force and what’s it do? What are Newton’s three laws of motion? What are they good for? Rosencrantz: “ Heads. Heads. Heads. Heads. …” Rosencrantz and Guildenstern are Dead by Stoppard Lecture 2, Newton’s Laws Phys 100, How Things Work
What Newton said:
1: Objects have inertia Motion under no force does not change momentum is constant 2: F = ma aka (force) = (mass)×(acceleration) if you push on something you can change its motion decrease, increase or re-direct the momentum 3: Each (action) force causes and equal and opposite reaction F (A on B) = − F (B on A) Lecture 2, Newton’s Laws^ Phys 100, How Things Work
Vectors
There is more than one spatial direction Write boldface or symbols with arrows F Position r (or whatever) Velocity v Acceleration a Force F Lecture 2, Newton’s Laws^ Phys 100, How Things Work
Remedial Vector Vocabulary
- Cartesian components (the x, y and z or direction of it)
- Length or amplitude (the amount of it) r 2 r 1 Δ r Add them “head to tail” graphically Or: r 1 + Δr = r 2 and v = vx + vy = ivx + jvy Lecture 2, Newton’s Laws^ Phys 100, How Things Work
An example
- Pop fly chased by Ozzie Smith
- Horizontal speed is constant
- Vertical speed changes
- Acceleration is down And constant Lecture 2, Newton’s Laws^ Phys 100, How Things Work
Now back to Newton’s laws
Newton 2: F = ma Force is gravity or weight and constant here So: (drum roll…..) Acceleration is constant it’s 9.8m/s^2 it points down Only vy changes, vx is constant y x
Lecture 2, Newton’s Laws Phys 100, How Things Work
More of the example
For constant acceleration Horizontal component x = x 0 + vxΔt Vertical component y = y 0 + vyΔt + ay (Δt)^2 / Both components r = r 0 + vΔt + a(Δt)^2 / y Velocity v = v 0 + aΔt x Lecture 2, Newton’s Laws Phys 100, How Things Work
Physics is problems solving
- How high does the ball go if the initial vy is 30m/s?
- How far does Ozzie run to catch it if the initial vx is 10m/s?
- How long is the ball in the air?
- Is Ozzie amazing or what?
- How can you solve these kinds of questions?
- Write down the definitions (what does vy mean?)
- Write down the principles (F = ma for example)
- Analyze the problem to get the answer Lecture 2, Newton’s Laws^ Phys 100, How Things Work
Let’s try one
- How high does the ball go?
- Write down the definitions vy = Δy/ Δt a = vy = Δvy/ Δt
- Write down the principles y = y 0 + v0yΔt + ay(Δt)^2 / v = v 0 + aΔt, which means vy = v0y + ayΔt Lecture 2, Newton’s Laws^ Phys 100, How Things Work
Now analyze the problem
Use what we know to get what we want (in stages) So we can use vy = v0y + ayΔt to get Δt And then use y = y 0 + v0yΔt + ay(Δt)^2 / 2 to get y at the top of the arc We know v0y (30m/s) and ay (-10m/s^2 ), but not vy and Δt vy = 0 at the top of the arc, so 0 = (30m/s) + (-10m/s^2 )Δt and hence Δt = 3 seconds y = y 0 + v0yΔt + ay(Δt)^2 / 2 = 0 + (30)(3) + (-10)(3^2 )/ = 45 m Lecture 2, Newton’s Laws^ Phys 100, How Things Work
How long is the ball in the air?
- Can do more calculations or can think for a moment.
- Equations for motion are the same going up and coming down.
- So from symmetry, expect time to come down to be the same.
- Total time in the air is 3 + 3 = 6 sec
- Symmetry is a new principle. Lecture 2, Newton’s Laws^ Phys 100, How Things Work
How far does Ozzie run?
- At most, he runs for 6 sec at 10 m/sec (world record speed)
- And yes: He was amazing - the best ever at short
- Probably less depending on where the ball was hit on the field.
- I did not tell you enough to answer this one. You don’t know where he starts or where the ball is headed
Lecture 2, Newton’s Laws Phys 100, How Things Work
Ramps allow work to be spread out
Work to lift the boulder is (W)(Δy) = mg(y-y 0 ) You’re tired at the top of the ramp because you gave your energy to the boulder’s potential energy You push against the force W(Δy)/[(Δx)^2 + (Δy)^2 ]1/ which is always smaller than W The ramp gives you a mechanical advantage. You do the same work with less effort over a longer distance Δy Δx
W
The mammoth’s headache comes from releasing that potential energy as kinetic energy Lecture 2, Newton’s Laws Phys 100, How Things Work
Take home messages
- Newton 2 (and 3)
- Equations of motion
- HOW TO SOLVE PROBLEMS !!!!
- Definitions
- Principles
- Analysis
- Ramps and mechanical advantage
- Potential energy
- Kinetic energy
