1. Applications of Newton’s Laws
Chapter 6
Applications of Newton’s Laws

2. Midterm Test #1 - Thursday!
21 multiple-choice problems
A calculator will be needed.
CHECK YOUR BATTERIES!
NO equations or information may be stored in your calculator. This is part of your pledge on the exam.
Scratch paper will be provided, to be turned in at the end of the exam.
A sign-in sheets will be used, photographs of the class will be taken, all test papers will be collected

3. Frictional Forces
Friction has its basis in surfaces that are not completely smooth:

4. Kinetic friction
Kinetic friction: the friction experienced by surfaces sliding against one another
The frictional force is proportional to the contact force between the two surfaces (normal force):
The constant is called the coefficient of kinetic friction.
fk always points in the direction opposing motion of two surfaces 4

5. Frictional Forces fk
Naturally, for any frictional force on a body, there is an opposing reaction force on the other body

6. fk fs Frictional Forces static friction
when relative motion stops, surfaces settle into one another
static friction
when moving, one bumps “skip” over each other

7. Static Friction
The static frictional force tries to keep an object from starting to move when other forces are applied.
The static frictional force has a maximum value, but
may take on any value from zero to the maximum... depending on what is needed to keep
the sum of forces to zero.
The maximum static frictional force is also proportional to the contact force

8. Static Friction
A block sits on a flat table. What is the force of static friction?
a) zero
b) infinite
c) you need to tell me stuff, like the mass of the block, μs, and what planet this is happening on

9. Characteristics of Frictional Forces
Frictional forces always oppose relative motion
Static and kinetic frictional forces are independent of the area of contact between objects
Kinetic frictional force is also independent of the relative speed of the surfaces.
Coefficients of friction are independent of the mass of objects, but in (most) cases forces are not:
(twice the mass
= twice the weight
= twice the normal force
= twice the frictional force)

10. Coefficients of Friction
Q: what units?

11.   Measuring static coefficient of friction
If the block doesn’t move, a=0.
Given the “critical angle” at which the block starts to slip, what is μs? x y N W fs Wx Wy
at the critical point  

12.   Acceleration of a block on an incline y x N W v
If the object is sliding down - x y v N W fk Wx Wy  

13.   Acceleration of a block on an incline y x N
If the object is sliding up - x y v N Wx Wy fk
What will happen when it stops?  W 

14. Sliding Down II
A mass m is placed on an inclined plane ( > 0) and slides down the plane with constant speed. If a similar block (same ) of mass 2m were placed on the same incline, it would:
a) not move at all
b) slide a bit, slow down, then stop
c) accelerate down the incline
d) slide down at constant speed
e) slide up at constant speed
Answer: d m

15. Sliding Down II
A mass m is placed on an inclined plane ( > 0) and slides down the plane with constant speed. If a similar block (same ) of mass 2m were placed on the same incline, it would:
a) not move at all
b) slide a bit, slow down, then stop
c) accelerate down the incline
d) slide down at constant speed
e) slide up at constant speed  W N f Wx Wy
The component of gravity acting down the plane is double for 2m. However, the normal force (and hence the friction force) is also double (the same factor!). This means the two forces still cancel to give a net force of zero.

16. Tension
When you pull on a string or rope, it becomes taut. We say that there is tension in the string.
Note: strings are “floppy”, so force from a string is along the string!

17. Tension is the same everywhere in a massless rope!
Tension in a chain
Tup = Tdown
when W = 0 W
Tup
Tdown
In this class: we will assume that all ropes, strings, wires, etc. are massless unless otherwise stated.
Tension is the same everywhere in a massless rope!

18. Massive vs. Massless Rope
The tension in a real rope will vary along its length, due to the weight of the rope.
T3 = mg + Wr
In this class: we will assume that all ropes, strings, wires, etc. are massless unless otherwise stated.
T2 = mg + Wr/2
T1 = mg
Tension is the same everywhere in a massless rope! m

19. Three Blocks
Three blocks of mass 3m, 2m, and m are connected by strings and pulled with constant acceleration a. What is the relationship between the tension in each of the strings?
a) T1 > T2 > T3
b) T1 < T2 < T3
c) T1 = T2 = T3
d) all tensions are zero
e) tensions are random a T3 T2 T1 3m 2m m

20. Three Blocks
Three blocks of mass 3m, 2m, and m are connected by strings and pulled with constant acceleration a. What is the relationship between the tension in each of the strings?
a) T1 > T2 > T3
b) T1 < T2 < T3
c) T1 = T2 = T3
d) all tensions are zero
e) tensions are random
T1 pulls the whole set of blocks along, so it must be the largest. T2 pulls the last two masses, but T3 only pulls the last mass. a T3 T2 T1 3m 2m m
Follow-up: What is T1 in terms of m and a?

21. Tension
Force is always along a rope Ty T T W

22. Idealization: The Pulley
An ideal pulley is one that simply changes the direction of the tension
distance box moves = distance hands move
speed of box = speed of hands
acceleration of box = acceleration of hands

23. Tension in the rope?

24. 2.00 kg
Tension in the rope? W T

25. y :
m1 : x :
m2 : y : μk fk μk μk μk

26. Over the Edge m m a a F = 98 N Case (1) Case (2)
In which case does block m experience a larger acceleration? In case (1) there is a 10 kg mass hanging from a rope and falling. In case (2) a hand is providing a constant downward force of 98 N. Assume massless rope and frictionless table.
a) case (1)
b) acceleration is zero
c) both cases are the same
d) depends on value of m
e) case (2) m a
F = 98 N m a
10 kg
Case (1)
Case (2) 26

27. Over the Edge m m a a F = 98 N Case (1) Case (2)
In which case does block m experience a larger acceleration? In case (1) there is a 10 kg mass hanging from a rope and falling. In case (2) a hand is providing a constant downward force of 98 N. Assume massless rope and frictionless table.
a) case (1)
b) acceleration is zero
c) both cases are the same
d) depends on value of m
e) case (2) m a
F = 98 N
In case (2) the tension is 98 N due to the hand. In case (1) the tension is less than 98 N because the block is accelerating down. Only if the block were at rest would the tension be equal to 98 N. m a
10 kg
Case (1)
Case (2) 27

28. Springs
Hooke’s law for springs states that the force increases with the amount the spring is stretched or compressed:
The constant k is called the spring constant.

29. Springs
Note: we are discussing the force of the spring on the mass. The force of the spring on the wall are equal, and opposite.

30. Springs and Tension a) (L1 + L2) / 2 b) L1 or L2, whichever is smaller
A mass M hangs on spring 1, stretching it length L1
Mass M hangs on spring 2, stretching it length L2
Now spring1 and spring2 are connected end-to-end, and M1 is hung below. How far does the combined spring stretch?
a) (L1 + L2) / 2
b) L1 or L2, whichever is smaller
c) L1 or L2, whichever is bigger
d) depends on which order the springs are attached
e) L1 + L2

31. Springs and Tension a) (L1 + L2) / 2 b) L1 or L2, whichever is smaller
A mass M hangs on spring 1, stretching it length L1
Mass M hangs on spring 2, stretching it length L2
Now spring1 and spring2 are connected end-to-end, and M1 is hung below. How far does the combined spring stretch?
a) (L1 + L2) / 2
b) L1 or L2, whichever is smaller
c) L1 or L2, whichever is bigger
d) depends on which order the springs are attached
e) L1 + L2 W
Fs=T

32. Springs and Tension a) (L1 + L2) / 2 b) L1 or L2, whichever is smaller
A mass M hangs on spring 1, stretching it length L1
Mass M hangs on spring 2, stretching it length L2
Now spring1 and spring2 are connected end-to-end, and M1 is hung below. How far does the combined spring stretch?
a) (L1 + L2) / 2
b) L1 or L2, whichever is smaller
c) L1 or L2, whichever is bigger
d) depends on which order the springs are attached
e) L1 + L2 W
Fs=T
Spring 1 supports the weight.
Spring 2 supports the weight.
Both feel the same force, and
stretch the same distance as before.