Mass vs Weight Mass (m) – amount of matter in an object Mass (m) – amount of matter in an object It’s what provides the object’s inertia, It’s what provides the object’s inertia, It’s a constant no matter where it is measured It’s a constant no matter where it is measured Units: grams – standard in chemistry – think paperclip (slug) Units: grams – standard in chemistry – think paperclip (slug) kg – standard in physics – 1000 g – think textbook kg – standard in physics – 1000 g – think textbook Volume (V) – amount of space object takes up Volume (V) – amount of space object takes up Units: liter, cm 3, m 3, (gal, cup, in 3 ) Recall Density = m/V it is the mass to volume ratio Recall Density = m/V it is the mass to volume ratio Weight (W) – the force of gravity on an object Weight (W) – the force of gravity on an object it’s how much gravity pulls on the mass of the object it’s how much gravity pulls on the mass of the object so depending on what the gravity is in your location, your weight will vary so depending on what the gravity is in your location, your weight will vary Units: Newton, (lbs) Units: Newton, (lbs) So while m ≠ W, they are proportional (m α W) if measured in the same location.

The Math of Mass vs Weight eq’n: W = mg where on Earth, g = 9.8 m/s 2, down units: N = kg m/s 2 So a Newton is a derived unit, just like m/s or m/s 2. derived unit – any unit which is a combination of any of the fundamental units like meter, sec, kg… but unlike m/s, it was a bit cumbersome to say, so we gave it a nickname, that honored Issac Newton. Note, DO NOT USE 1 kg = 9.8 N ! (since a kg should never be set = to a N) so it is bad form to use this as a conversion factor to get from mass to Weight

Tools to Measure Mass vs Weight Spring scales – contain a spring that extends or compresses depending upon how much push or pull is applied – so they’re location ___________ - so they’re good to measure ____ Spring scales – contain a spring that extends or compresses depending upon how much push or pull is applied – so they’re location ___________ - so they’re good to measure ____Ex: Balances – compare the amount of material in one object with the amount in another – so they’re location ___________ - so they’re good to measure _____ Balances – compare the amount of material in one object with the amount in another – so they’re location ___________ - so they’re good to measure _____Ex: But whether you’re measuring mass or weight is very confusing to keep straight and often messed up in real life – even by people of science! Ex: “scale” at dr’s office … in lbs “weigh” your sample of ____ in grams in chemistry “weigh” your sample of ____ in grams in chemistry

Net Force Net force (F net ) - the vector sum (both mag & direction) of all the forces acting on an object at one time Last chapter we called this Resultant Force – F R Last chapter we called this Resultant Force – F R If an object’s F net = 0, then the object satisfies the condition in Newton’s 1 st Law to be maintaining its state of motion If an object’s F net = 0, then the object satisfies the condition in Newton’s 1 st Law to be maintaining its state of motion - either at rest or constant velocity… So we say it is in a state of equilibrium So we say it is in a state of equilibrium the object CAN be moving, just constantly the object CAN be moving, just constantly there can be lots of forces acting on it, as long as they cancel each other to add to 0 there can be lots of forces acting on it, as long as they cancel each other to add to 0 Let’s look at a few examples:

1 st consider a book sitting on a table What are the forces acting on it? The Earth pulls down – force of gravity – W The Earth pulls down – force of gravity – W The table pushes up – force of support – F N The table pushes up – force of support – F N [Note: F N is the normal (perpendicular) force – the force of support an object gets from the surface on which it rests – it is always  to the surface, so but also ] free body diagram: So, back to the book, which is in equilibrium, since it’s maintaining its state of motion (at rest) F net = F N + W = 0 F net = F N + W = 0 which means F N = - W they are = magnitudes, but opposite direction!

2 nd consider a block hung from a string What are the forces acting on it? The Earth pulls down – force of gravity – W The Earth pulls down – force of gravity – W The string pulling up – force of tension – T The string pulling up – force of tension – T [Note: T is the supporting force applied to an object through a long, stringy thing like ] FBD: So, back to the block, which is in equilibrium, since it’s maintaining its state of motion F net = T + W = 0 F net = T + W = 0 which means T = - W they are = mags, but opposite direction again.

3 rd consider a block hung from two vertical strings: What are the forces acting on it? The Earth pulls down – force of gravity – W The Earth pulls down – force of gravity – W The strings pull up – 2 forces of tension – T 1 & T 2 The strings pull up – 2 forces of tension – T 1 & T 2FBD once again, the block is in equilibrium, so F net = T 1 + T 2 + W = 0 F net = T 1 + T 2 + W = 0 which means T 1 + T 2 = - W Are T 1 & T 2 equal to each other? Most likely yes in this situation, but always? Not necessarily – depends on how / where they’re attached to the object and if the object is made of a uniform material or not.

4 th consider a block hung from 2 angled strings: Both string’s tensions/scale’s readings get greater as the angles get wider, but why? Since the tensions are angled, only the vertical component of each actually pulls straight up to support the weight of the object. Now these 2 components, T 1V & T 2V, take on the values that the scales had when they simply hung vertically. Since the tensions are angled, only the vertical component of each actually pulls straight up to support the weight of the object. Now these 2 components, T 1V & T 2V, take on the values that the scales had when they simply hung vertically. See Figure 1 And the more horizontal the strings/scales are, the more tension has to be put into the strings/scales along the hypotenuse to keep the vertical component of it big enough to continue balancing the weight of the block, downward. And the more horizontal the strings/scales are, the more tension has to be put into the strings/scales along the hypotenuse to keep the vertical component of it big enough to continue balancing the weight of the block, downward.

The horizontal components don’t help to support the weight at all, and in fact always cancel each other out: The horizontal components don’t help to support the weight at all, and in fact always cancel each other out: T 1H = - T 2H T 1H = - T 2H Therefore, the resultant forces, T 1 & T 2, would have to be larger than either of their components. Therefore, the resultant forces, T 1 & T 2, would have to be larger than either of their components. and bigger than when they were simply pulling straight up, as in 3 rd example. The readings on the scales, T 1 & T 2, & their vertical components, T 1V & T 2V, only equal each other The readings on the scales, T 1 & T 2, & their vertical components, T 1V & T 2V, only equal each other (T 1 = T 2 and T 1V = T 2V ) (T 1 = T 2 and T 1V = T 2V ) if the supports are at equal angles.

The more vertical string/scale has the greater tension… but why? the more vertical support has the larger vertical component and therefore does more (has > T) to support the weight the more vertical support has the larger vertical component and therefore does more (has > T) to support the weight but the vertical components will still add to equal the weight of the object : T 1V + T 2V = - W but the vertical components will still add to equal the weight of the object : T 1V + T 2V = - W and the horizontal components will still be equal but opposite to each other: T 1H = -T 2H and the horizontal components will still be equal but opposite to each other: T 1H = -T 2H Note: the string’s length does not determine the amount of tension in it! 5 th consider a block hung from 2 unequally angled strings:

6 th consider a block hung from two scales in a row Both scales read the entire weight of the object they hold, with the top one reading just a bit more, as it is holding up the 2 nd scale, as well as the object.