1. Physics 106 Lesson #1 Mass and Weight Dr. Andrew Tomasch 2405 Randall Lab atomasch@umich.edu

2. Mechanics: The Big Picture  Kinematics: How objects move  Dynamics: Why objects move  Energy and momentum  Fluids (Resting and moving)  Oscillations and Waves  How does the mechanical world work? Johannes Kepler Galileo Galiliei Isaac Newton

3. How to describe motion? –Measurements → Physical Quantities –Requires units → Système International (SI) units: Units for Physics SICGSBE Lengthmeter (m)centimeter (cm)foot (ft) Masskilogram (kg)gram (g)slug (sl) Timesecond (s) PrefixFact.Symb.Common name Giga-10 9 GBillion Mega-10 6 MMillion Kilo-10 3 kThousand Centi-10 -2 cHundredth Milli-10 -3 mThousandth Micro-10 -6  Millionth Nano-10 -9 nBillionth SI units are also called MKS units for Meters, Kilograms and Seconds

4. Scalars: magnitude only (ex: radius R =10 cm) Vectors: magnitude and direction –Arrow length ≡ magnitude of the vector –Arrow direction ≡ vector direction Example: Displacement ≡ = 1 m to the right magnitude direction Two Quantities: Scalars & Vectors 1 m

5. Mass and Weight Mass (or inertia) is an intrinsic property of matter. Mass is a scalar. Weight is an attractive force exerted by the Earth on an object in accordance with Newton’s Universal Law of Gravitation. Weight is a vector with a magnitude equal to the product of mass and the acceleration of gravity ( mg ) directed toward the Earth’s Center, a direction we perceive as “downward” toward the Earth’s surface. Weight depends on the properties of the gravitating body (radius and mass) and is therefore different on different planets. On Earth the acceleration of gravity has a value of g = 9.8 m/s 2. On the moon the acceleration approximately 1/6 that at the Earth’s Surface

6. Spring Scales Springs can be used to make simple scales Spring scales measure weight by means of Hooke’s Law which states that the force required to stretch a spring is proportional to the distance the spring stretches. The constant of proportionality between the applied force and the distance the spring stretches is called the spring constant or force constant of the spring. Attaching a pointer to a spring and observing the amount the spring stretches with a weight hanging on it provides a direct measure of the weight (force) acting on the spring. Since weight near the Earth’s surface is proportional to the mass of an object ( W = mg ), scales can also be calibrated in units of mass (grams, kilograms) rather than in units of force (Newtons, pounds)

7. Hooke’s Law for Springs An applied force stretches a spring: spring constant or force constant units: N/m Robert Hooke 1635-1703 “The force required to stretch a spring is proportional to the distance the spring stretches” Equivalently, the amount a spring stretches is proportional to the applied force: x = F/k Hooke’s Law works for compressed springs too

8. The Free Body Diagram (FBD) A “cartoon” used to understand the forces acting on an object Only the object and the forces acting on it are shown A powerful conceptual tool for understanding the net (total) force acting on an object, which in turn determines its motion Because the washer is at rest the net (total) force on it is zero Washer Weight W = mg Spring Force F s = kx