Motion: Forces influence motion How do we describe motion? Displacement Velocity Acceleration
Position & Displacement The position (r) of an object describes its location relative to some origin or other reference point. The displacement is the change in an object’s position. It depends only on the beginning and ending positions. Δ is a symbol. Δr does not mean Δ times r
Vector Subtraction • A-B = A+(- B) • -B same magnitude as B but opposite direction • B-A =-( A- B) The order matters
y r3 r r2 x r1 Example (text problem 3.4): Margaret walks to the store using the following path: 0.500 miles west, 0.200 miles north, 0.300 miles east. What is her total displacement? Give the magnitude and direction. Take north to be in the +y direction and east to be along +x. r2
y r ry x rx Example continued: The displacement is r = rf ri. The initial position is the origin; what is rf? The final position will be rf = r1 + r2 + r3. The components are rfx = r1 + r3 = 0.2 miles and rfy = +r2 = +0.2 miles. Using the figure, the magnitude and direction of the displacement are N of W.
What distance did Margaret walk? • This is not the same as her displacement • Why? • Is displacement a Vectoror scalar? • Is distance a Vector or scalar? • Think of hitting a home run. What is the displacement? What is the distance the runner travels?
Velocity Velocity is a vector that measures how fast and in what direction something moves. Δ is a symbol it is not a quantity Speed is the magnitude of the velocity. It is a scalar.
Velocity The velocity is a vector. It changes if we change • the speed • the direction i.e. driving around a curve even at constant speed.
Fig. 03.09 T = 12 seconds
finish Path of a particle r Start vav is the constant speed that results in the same displacement in a given time interval.
At what point of the butterfly’s path does the velocity change? • At almost every point • Only at the beginning and end • It is constant the whole time • We can’t tell unless we know the speed everywhere.
y r3 r r2 x r1 Example (text problem 3.4): Margaret walks to the store using the following path: 0.500 miles west, 0.200 miles north, 0.300 miles east. What is her total displacement? Give the magnitude and direction. Take north to be in the +y direction and east to be along +x.
Example: Consider Margaret’s walk to the store in the earlier example. If the first leg of her walk takes 10 minutes, the second takes 8 minutes, and the third 7 minutes, compute her average velocity and average speed during each leg and for the overall trip. Use the definitions:
Instantaneous velocity If Δt becomes very small we call v the instantaneous velocity Your speedometer reads instantaneous speed
x (m) x2 x1 t2 t1 t (sec) On a graph of position versus time, the average velocity is represented by the slope of a chord.
x (m) t (sec) This is represented by the slope of a line tangent to the curve on the graph of an object’s position versus time.
As you drive around a corner you are careful to keep the speedometer reading at 30 km/hr. You have been moving at • Constant speed • Constant velocity • Both constant speed and velocity • Neither constant speed nor constant velocity
Finding d when we know v Consider only x component Δx = vxΔt If vx = v1(constant) This is the same as the area in graph of v /t
The instantaneous velocity points tangent to the path. vi r vf ri rf Points in the direction of r A particle moves along the gold path as shown. At time t1 its position is ri and at time t2 its position is rf. y x
Example (text problem 3.24): Speedometer readings are obtained and graphed as a car comes to a stop along a straight-line path. How far does the car move between t = 0 and t = 16 seconds? Since there is not a reversal of direction, the area between the curve and the time axis will represent the distance traveled.
acceleration Acceleration is a vector (since v is a vector)
Which has a greater acceleration an airplane going from 1000 km/hr to 1005 km/hr in 5 seconds or a skateboarder going from 0 to 5 km/hr in 1 second? • The airplane • The skateboarder
Example (text problem 3.39): If a car traveling at 28 m/s is brought to a full stop 4.0 s after the brakes are applied, find the average acceleration during braking. Given: vi = +28 m/s, vf = 0 m/s, and t = 4.0 s.
Points in the direction of v. v vf ri rf The instantaneous acceleration can point in any direction. A particle moves along the gold path as shown. At time t1 its position is ri and at time t2 its position is rf. y vi x
Motion: Forces influence motion How do we describe motion? F =ma
Exam! • Monday Oct. 5 • Up to and including today’s lecture • Review
Question • You put your notebook on the front seat of your car. When your car stops, the notebook slides off forward. Why? A) A net force acted on it. B) No net force acted on it. C) It remained at rest. D) It didn't move, but only seemed to. E) Gravity briefly stopped acting on it.
Question • A book is sitting on a desk top. Identify the 3rd law partner of the weight of the book. A) The force of the desk on the book. B) The force of the book on the desk. C) The force of the earth on the book. D) The force of the book on the earth.
Question • A box of mass m sits on an inclined plane. What is the relationship between the weight of the box, W, and the normal force exerted on the box, N? • A) W > N • B) W = N • C) W < N • D) can't tell
Question • For which arrangement of (moving) boxes is the force of friction larger? The two boxes are identical. A) The stacked boxes. (1) B) The side-by-side boxes (2). C) The force is the same.
acceleration Acceleration is a vector Δv= a Δt
y (north) vi vf x (east) Example (text problem 3.47): At the beginning of a 3 hour trip you are traveling due north at 192 km/hour. At the end, you are traveling 240 km/hour at 45 west of north. (a) Draw the initial and final velocity vectors. 450
Find Δv Find aav
Which of the following controls can be used to accelerate your car? A) Gas pedal B) Brake C) Steering wheel D) All of the above
Newton’s 2nd Law The acceleration of a body is directly proportional to the net force acting on the body and inversely proportional to the body’s mass. Mathematically:
An object’s mass is a measure of its inertia. The more mass, the more force is required to obtain a given acceleration. • If F is fixed and m is doubled a is • Doubled • Halved • Remains the same • What should F be if a is to be the same? • What if m is halved?
The net force is just the vector sum of all of the forces acting on the body, often written as F. If a = 0, then F = 0. This body can have: Speed = 0 which is called static equilibrium, or speed 0, but constant and same direction, which is called dynamic equilibrium.