Chapter 4 – Forces and the Laws of Mo5on
Sec5on 1 – Changes in Mo5on
System:
- object or set of objects under study
Environment/surroundings:
- everything in the universe outside of the system
Types of Forces:
- contact : things touching
: includes fric5on and air resistance
- non-contact or field : long-range
: includes gravity, electromagne5c forces and nuclear forces
Forces:
- push or pull
- measured in Newtons (1 N = 1 kgm/s2)
- force is a vector (yeah! Vector addi5on!)
Free Body Diagrams:
- illustra5ons to represent all forces ac5ng on an object
1) represent the system as a dot
2) draw arrows of forces ac5ng on the object in the direc5on of the force, star5ng at the object
3) make arrows propor5onal to magnitude of forces
e.g.1) Draw a free body diagram of a person standing on the ground.
e.g.2) Draw a free body diagram of a feather falling to the ground, experiencing air resistance.
e.g.3) Draw a free body diagram of a box res5ng on a table. The box has a 10 N cat siYng on top of it.
Sec5on 2 – Newton’s First Law
Iner5a:
- tendency for an object to remain in its current state
- “current state” means either sta5onary or moving with constant velocity
Mass:
- measure of amount of maber an object contains
- quan5fica5on of iner5a
- does not change regardless of situa5on/loca5on
Net Force:
- sum of all forces ac5ng on an object Fnet = Σ F
- recall: force is a vector
- should be based on FBD
e.g.4) An object is acted upon by 3 forces. The first is 5 N to the
North, the second is 5 N East, and the third is 3 N South. What is the net force ac5ng on the object?
e.g.5) Two dogs pull on a 5re. One pulls using 15 N of force directed 30 degrees above the horizontal and the second pulls using 10 N of force directed NW. What is the net force on the 5re?
prac5ce B page 126 #(1), 2, 3
(1) 60.6 N & 35.0 N
2) 2.48 N @ 295°
1st Law:
- An object at rest will remain at rest unless acted upon by a net external force. An object moving at constant velocity will remain at constant velocity unless acted upon by a net external force.
e.g.6) Why is it hard to understand the 2nd part of this law?
Equilibrium:
- an object is in equilibrium if it has a net force of 0 ac5ng on it
Sec5on 3 – Newton’s Second and Third Laws
2nd Law:
- an object’s accelera5on is propor5onal to the net force ac5ng on the object
Fnet = ma
- mass must be in kg and accelera5on must be in m/s2 to be
compa5ble with Newtons!
e.g.9) A 2.0 kg box is pushed by a force of 10 N East. What is its accelera5on?
e.g.10) The same 2.0 kg box is pushed with a 10 N force East, and a second 5.0 N force East. What is it’s accelera5on now?
e.g.11) A 2.0 N force brings an object that is ini5ally traveling 3.0 m/s East to a rest in 1.5 s. What is the mass of the object?
e.g.12) A 1.0 kg box is pushed along a flat, smooth table by two people. One person pushes 3.0 N East and the second pushes 3.0 N North.
a) What is the net force ac5ng on the box? b) What is the accelera5on of the box?
Prac5ce C page 130 #1-3, (4), 5 #1. 2.2 m/s2 forward
#2. 1.4 m/s2 North
#3. 4.50 m/s2 East
(#4.) 2.1 kg
Newton’s 3rd Law:
- for every ac5on, there is an equal and opposite reac5on
-the key to Newton’s 3rd law is that the original force and the
reac5on force act on different objects
- applies to non-contact (field) forces as well as contact forces
- some5mes, force diagrams (not FBD) are useful for looking at this
Sec5on 4 – Everyday Forces
Weight:
- force of gravity ac5ng on an object
W = mg
- changes depending on loca5on since g changes
e.g.14) What is the weight of a 5.0 kg bucket near the surface of the Earth? What is the mass of a 200 N crate near the surface of the Earth?
Normal Force:
- a force that acts on a surface in a direc5on perpendicular to the surface
- osen called apparent weight
- osen equal to the force of gravity ac5ng on a object – why?
Surface fric5on:
- arises from instantaneous forces between touching surfaces
- depends on the types of surfaces in contact
- depends on the force pushing the surfaces together (typically the weight of the upper object)
- does not depend on surface area of the surfaces in contact
- is calculated using Ff = μFN
where FN is the force pushing the objects together Ff is the force of fric5on
μ is the coefficient of fric5on (no units!)
Coefficient of Fric5on:
- there are 2 types, sta5c and kine5c
- experimentally determined, always given (or info to calculate)
e.g.16) Joe has a mass of 65 kg. What is the maximum
fric5onal force between his rubber-soled shoes and a concrete floor when he is sta5onary? When he slides on the floor?
Direc5on of Fric5on:
e.g.17) A box is pushed along a surface using a force of 20 N. Calculate the mass of the box if it moves at a constant 1.0 m/s. Assume it is a wooden box on a wooden floor.
e.g.18) A different box is pushed along a surface using a force of 20 N. If its accelera5on is 1.0 m/s2, what is the mass of the
box? Assume it is a wooden box on a wooden floor.
e.g.19) A 5.0 kg box is pulled along a horizontal floor, using a rope that is 5lted at 15 degrees above the horizontal. If the force in the rope is 100 N and the coefficient of kine5c fric5on
between the box and the floor is 0.35, what is the accelera5on of the box?
e.g.20) A boy pulls a toy horizontally along a rough table top. The toy has a mass of 100 g and accelerates at 1.2 m/s2, when he
applies a force of 0.56 N. Calculate the coefficient of fric5on between the table top and the toy.
prac5ce D page 137 #1, (2), 3 and Prac5ce E page 139 #1, 4
Prac5ce D: 1. 0.23
(2) a) 0.67; b) 0.52
3. a) 870 N; 670 N b) 110 N; 84 N c) 1000 N; 500 N d) 5 N; 2 N
Prac5ce E:
Inclined Planes:
- an inclined plane is any non-horizontal surface such as a ramp or a hill
- we rotate the xy coordinate plane so that the x-axis matches the plane surface, giving us components of gravity
Fgx = mgsinθ Fgy = mgcosθ
where Fgx is the component of the force of gravity pulling the object down the plane and Fgy is equal to the normal
e.g.21) What is the force pulling a 60 kg skier down a
fric5onless hill 5lted at 25 degrees with respect to the horizontal? What is the skier's accelera5on? What is the normal force ac5ng on the skier?
Fric5on on Inclined Planes:
- fric5on on an inclined plane opposes the direc5on of mo5on
e.g.23) What is the net force ac5ng on the same 60 kg skier on the same hill 5lted at 25 degrees with respect to the horizontal if the coefficient of fric5on between his skis and the snow is 0.10? What is the skier's accelera5on?
e.g.24) What is the accelera5on of the 2.0 kg box placed on the ramp 5lted at 30 degrees if the coefficient of fric5on is 0.20?
e.g.25) At what angle with respect to the horizontal must the plane in the previous example be 5lted in order for the box to not slide down the plane?
page 139 (2) 0.77 m/s2
3) a) 0.061 b) 3.6 m/s2
page 145 36) 0.436
48) a) 1.78 m/s2 b) 0.37 c) 9.4 N d) 2.67 m/s
Review: page 143 #2, 6, 8, (11), 12, 13, 19 explain, 21, 22, 26a,c, 32, 34 (read in chapter), (37), 39, 41, 43, 46, 49, (51), (54)
2. no, net force is zero 6. a) iner5a b) con5nue forward
8. On board (11) a) on board b) 220 N and 114 N
12. 4 N; 3 N 13. Because earth has a very large mass
19. a) 0 b) 0 21. 55 N
22. a) 770 N @ 82° b) 0.24 m/s2 @ 82°
26a) 54 N c) 49 N 32)increases normal force
34) Accelera5on decreases to zero
(37) 0.816 39. 1.0 m/s2 41. 13 N down
43.64 N up 46. 50 m 49. -1.2 m/s2 ; 0.12
Compare/Contrast Ac5vity:
Re-group with your original groups of 4. Switch partners so that each pair has one person who completed part I and one person who completed part II.
On the next right-hand page of your lab notebook aser your lab report, answer the following ques5ons in complete sentences.
1. What was the objec5ve of each lab procedure? How do they compare? (Venn
diagram)
2. Did you determine the same kind of coefficient of fric5on? Explain.
3. Which lab procedure is more reliable to produce more precise results?
Accurate results? Why?
4. Working together, construct a number line on which you clearly label both
partners’ average coefficient, as well as the range for the part I result based on the average devia5on. Can you say, based on this graphic, that the
