Page 1
Friction
Contents
1 FrictionasPartofContactForce . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1 Example 6.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Extra Example 6.1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 KineticFriction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1 Example 6.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Extra Example 6.2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 StaticFriction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.1 Example 6.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.2 Extra Example 6.3.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4 LawsofFriction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
5 WhyFrictionHappens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6 MeasuringFrictionintheLab . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.1 Horizontal Table Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.2 Inclined Table Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.3 Example 6.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.4 Extra Example 6.4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
7 RollingFriction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
8 WorkedOutExamples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
8.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
8.2 Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
8.3 Example 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
8.4 Example 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
8.5 Example 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
8.6 Example 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
8.7 Example 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
8.8 Example 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
8.9 Example 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
8.10 Example 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.11 Extra Example 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Page 2
Friction
Contents
1 FrictionasPartofContactForce . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1 Example 6.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Extra Example 6.1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 KineticFriction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1 Example 6.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Extra Example 6.2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 StaticFriction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.1 Example 6.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.2 Extra Example 6.3.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4 LawsofFriction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
5 WhyFrictionHappens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6 MeasuringFrictionintheLab . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.1 Horizontal Table Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.2 Inclined Table Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.3 Example 6.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.4 Extra Example 6.4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
7 RollingFriction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
8 WorkedOutExamples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
8.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
8.2 Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
8.3 Example 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
8.4 Example 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
8.5 Example 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
8.6 Example 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
8.7 Example 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
8.8 Example 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
8.9 Example 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
8.10 Example 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.11 Extra Example 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1 FrictionasPartofContactForce
When two objects touch each other, tiny electric forces act between their surfaces
because of charged particles, like electrons and protons. These forces create a push
or pull called the contact force. The contact forces between two objects are equal in
size but point in opposite directions, following Newtons third law (if A pushes B, B
pushes A back just as hard).
This contact force isnt always straight up or down from the surface. It can be split
into two parts: the normal force, which is perpendicular to the surface and stops
objects from sinking into each other, and friction, which is parallel to the surface and
resists sliding. Imagine a book on a table: the table pushes up to balance the books
weight(normalforce)andsidewaystostopitfromsliding(friction). Figure 6.1shows
this split, with the contact force
?
F having a normal part
?
N and a friction part
?
f.
Friction can happen between solids (like a box on a ?oor), a solid and a liquid (like a
boat in water), or even two liquids. This chapter focuses on friction between solids.
Page 3
Friction
Contents
1 FrictionasPartofContactForce . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1 Example 6.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Extra Example 6.1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 KineticFriction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1 Example 6.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Extra Example 6.2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 StaticFriction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.1 Example 6.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.2 Extra Example 6.3.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4 LawsofFriction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
5 WhyFrictionHappens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6 MeasuringFrictionintheLab . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.1 Horizontal Table Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.2 Inclined Table Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.3 Example 6.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.4 Extra Example 6.4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
7 RollingFriction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
8 WorkedOutExamples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
8.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
8.2 Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
8.3 Example 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
8.4 Example 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
8.5 Example 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
8.6 Example 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
8.7 Example 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
8.8 Example 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
8.9 Example 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
8.10 Example 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.11 Extra Example 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1 FrictionasPartofContactForce
When two objects touch each other, tiny electric forces act between their surfaces
because of charged particles, like electrons and protons. These forces create a push
or pull called the contact force. The contact forces between two objects are equal in
size but point in opposite directions, following Newtons third law (if A pushes B, B
pushes A back just as hard).
This contact force isnt always straight up or down from the surface. It can be split
into two parts: the normal force, which is perpendicular to the surface and stops
objects from sinking into each other, and friction, which is parallel to the surface and
resists sliding. Imagine a book on a table: the table pushes up to balance the books
weight(normalforce)andsidewaystostopitfromsliding(friction). Figure 6.1shows
this split, with the contact force
?
F having a normal part
?
N and a friction part
?
f.
Friction can happen between solids (like a box on a ?oor), a solid and a liquid (like a
boat in water), or even two liquids. This chapter focuses on friction between solids.
Page 4
Friction
Contents
1 FrictionasPartofContactForce . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1 Example 6.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Extra Example 6.1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 KineticFriction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1 Example 6.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Extra Example 6.2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 StaticFriction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.1 Example 6.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.2 Extra Example 6.3.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4 LawsofFriction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
5 WhyFrictionHappens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6 MeasuringFrictionintheLab . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.1 Horizontal Table Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.2 Inclined Table Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.3 Example 6.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.4 Extra Example 6.4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
7 RollingFriction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
8 WorkedOutExamples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
8.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
8.2 Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
8.3 Example 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
8.4 Example 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
8.5 Example 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
8.6 Example 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
8.7 Example 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
8.8 Example 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
8.9 Example 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
8.10 Example 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.11 Extra Example 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1 FrictionasPartofContactForce
When two objects touch each other, tiny electric forces act between their surfaces
because of charged particles, like electrons and protons. These forces create a push
or pull called the contact force. The contact forces between two objects are equal in
size but point in opposite directions, following Newtons third law (if A pushes B, B
pushes A back just as hard).
This contact force isnt always straight up or down from the surface. It can be split
into two parts: the normal force, which is perpendicular to the surface and stops
objects from sinking into each other, and friction, which is parallel to the surface and
resists sliding. Imagine a book on a table: the table pushes up to balance the books
weight(normalforce)andsidewaystostopitfromsliding(friction). Figure 6.1shows
this split, with the contact force
?
F having a normal part
?
N and a friction part
?
f.
Friction can happen between solids (like a box on a ?oor), a solid and a liquid (like a
boat in water), or even two liquids. This chapter focuses on friction between solids.
2.1 Example 6.2
A 20 kg box is pulled across a ?oor. The kinetic friction coef?cient is 0.25. Find the
friction force. Use g= 9.8m/s
2
.
Solution: The normal force balances the weight:
N = 20×9.8= 196N.
Friction force:
f
k
= µ
k
N = 0.25×196= 49N,
opposite to the pull.
2.2 Extra Example 6.2.1
A 10kgsledslidesonsnowwith µ
k
= 0.1. Whatsthefrictionforce? Useg = 10m/s
2
.
Solution:
N = 10×10= 100N.
f
k
= 0.1×100= 10N.
3 StaticFriction
Static friction keeps objects from sliding when theyre touching but not moving, like
a heavy box youre pushing that stays still. It adjusts itself to match the push or pull
up to a limit, called the limiting friction:
f
max
= µ
s
N,
where µ
s
is the static friction coef?cient, usually a bit bigger than µ
k
. If you push
harder than this limit, the object starts sliding. Figure 6.7 shows a heavy cabinet
pushed left; the ?oor pushes right with static friction to keep it still. Static friction
can be any value up to f
max
to stop motion.
4
Page 5
Friction
Contents
1 FrictionasPartofContactForce . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1 Example 6.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Extra Example 6.1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 KineticFriction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1 Example 6.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Extra Example 6.2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 StaticFriction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.1 Example 6.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.2 Extra Example 6.3.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4 LawsofFriction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
5 WhyFrictionHappens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6 MeasuringFrictionintheLab . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.1 Horizontal Table Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.2 Inclined Table Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.3 Example 6.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.4 Extra Example 6.4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
7 RollingFriction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
8 WorkedOutExamples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
8.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
8.2 Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
8.3 Example 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
8.4 Example 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
8.5 Example 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
8.6 Example 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
8.7 Example 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
8.8 Example 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
8.9 Example 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
8.10 Example 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.11 Extra Example 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1 FrictionasPartofContactForce
When two objects touch each other, tiny electric forces act between their surfaces
because of charged particles, like electrons and protons. These forces create a push
or pull called the contact force. The contact forces between two objects are equal in
size but point in opposite directions, following Newtons third law (if A pushes B, B
pushes A back just as hard).
This contact force isnt always straight up or down from the surface. It can be split
into two parts: the normal force, which is perpendicular to the surface and stops
objects from sinking into each other, and friction, which is parallel to the surface and
resists sliding. Imagine a book on a table: the table pushes up to balance the books
weight(normalforce)andsidewaystostopitfromsliding(friction). Figure 6.1shows
this split, with the contact force
?
F having a normal part
?
N and a friction part
?
f.
Friction can happen between solids (like a box on a ?oor), a solid and a liquid (like a
boat in water), or even two liquids. This chapter focuses on friction between solids.
2.1 Example 6.2
A 20 kg box is pulled across a ?oor. The kinetic friction coef?cient is 0.25. Find the
friction force. Use g= 9.8m/s
2
.
Solution: The normal force balances the weight:
N = 20×9.8= 196N.
Friction force:
f
k
= µ
k
N = 0.25×196= 49N,
opposite to the pull.
2.2 Extra Example 6.2.1
A 10kgsledslidesonsnowwith µ
k
= 0.1. Whatsthefrictionforce? Useg = 10m/s
2
.
Solution:
N = 10×10= 100N.
f
k
= 0.1×100= 10N.
3 StaticFriction
Static friction keeps objects from sliding when theyre touching but not moving, like
a heavy box youre pushing that stays still. It adjusts itself to match the push or pull
up to a limit, called the limiting friction:
f
max
= µ
s
N,
where µ
s
is the static friction coef?cient, usually a bit bigger than µ
k
. If you push
harder than this limit, the object starts sliding. Figure 6.7 shows a heavy cabinet
pushed left; the ?oor pushes right with static friction to keep it still. Static friction
can be any value up to f
max
to stop motion.
4
3.1 Example 6.3
A 30 kg boy sits on a horse that accelerates at 2.0 m/sš. (a) If he doesnt slide back,
whats the friction force? (b) If he slides back, whats the maximum µ
s
? Use g =
10m/s
2
.
Solution: (a) Forces on the boy: weight, normal force, and friction f
s
. If he doesnt
slide, he accelerates with the horse:
f
s
= ma = 30×2.0= 60N.
(b) If he slides, the maximum friction wasnt enough:
f
max
= µ
s
N = µ
s
×30×10= 300µ
s
N.
300µ
s
< 60 =? µ
s
<
60
300
= 0.20.
3.2 ExtraExample 6.3.1
A 15 kg crate needs a 45 N force to start sliding on a ?oor. Find µ
s
. Use g= 10m/s
2
.
Solution:
N = 15×10= 150N, f
max
= 45N.
µ
s
=
45
150
= 0.30.
4 LawsofFriction
Here are the main rules for friction:
1. Whenobjectsslide, kineticfrictionis f
k
= µ
k
N, oppositetotheslidingdirection
relative to the other object.
2. When objects dont slide, static friction is f
s
= µ
s
N, adjusting to prevent sliding.
3. Friction doesnt depend on the contact area if the normal force stays the same.
Table 6.1 shows some friction coef?cients:
Table 1: Approximate Friction Coef?cients
Material µ
s
Material µ
s
Steel and steel 0.58 Copper and copper 1.60
Steel and brass 0.35 Te?on and te?on 0.04
Glass and glass 1.00 Rubber tyre on dry concrete 1.0
Wood and wood 0.35 Rubber tyre on wet concrete 0.7
Wood and metal 0.40 Ice and ice 0.10
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