AP

PHYS

Warm Up (10/26/15) — FrictionA trained sea lion slides from rest with constant acceleration down a 3.0 m long ramp into a pool of water. If the ramp is inclined at an angle of 23° above the horizontal and the coefficient of kinetic friction is 0.26, how long does it take for the sea lion to make a splash in the pool.

Fnet = ma; system: sea lion

Fg + Fk,fr + FN = ma

AP

PHYS

Warm Up (10/26/15) — FrictionA trained sea lion slides from rest with constant acceleration down a 3.0 m long ramp into a pool of water. If the ramp is inclined at an angle of 23° above the horizontal and the coefficient of kinetic friction is 0.26, how long does it take for the sea lion to make a splash in the pool.

Fnet = ma; system: sea lion

Fg + Fk,fr + FN = ma(−mgCosθ + FN),N + (mgSinθ − Fk,fr), E = ma

d = vo⋅t + ½a⋅t20

(−mgCosθ + FN) = 0 & (mgSinθ − Fk,fr) = ma

(mgSinθ − μk⋅FN) = m(2d ⁄ t2) FN = mgCosθ

AP

PHYS

Warm Up (10/26/15) — FrictionA trained sea lion slides from rest with constant acceleration down a 3.0 m long ramp into a pool of water. If the ramp is inclined at an angle of 23° above the horizontal and the coefficient of kinetic friction is 0.26, how long does it take for the sea lion to make a splash in the pool.

Fnet = ma; system: sea lion

Fg + Fk,fr + FN = ma

(−mgCosθ + FN),N + (mgSinθ − Fk,fr), E = ma (−mgCosθ + FN) = 0 & (mgSinθ − Fk,fr) = ma

d = vo⋅t + ½a⋅t20

(mgSinθ − μk⋅FN) = m(2d ⁄ t2) FN = mgCosθ

Daily Quiz #4 (10/27/15) — FrictionA block is placed on a rough surface inclined relative to the horizontal as shown in the figure. The incline angle is increased until the block starts to move. If the coefficient of static friction μs is 0.25, what is the weight of the block?

AP

PHYS

Fg

FN

θ

Fnet = ma; system: block

Fg + Fs,fr + FN = ma

θ

Fs,fr

Daily Quiz #4 (10/27/15) — FrictionA block is placed on a rough surface inclined relative to the horizontal as shown in the figure. The incline angle is increased until the block starts to move. If the coefficient of static friction μs is 0.25, what is the weight of the block?

AP

PHYS

Fg

FN

θ

θ

Fs,fr

Fnet = ma; system: block

Fg + Fs,fr + FN = ma

(−mgCosθ + FN),N + (mgSinθ − Fs,fr), E = ma 0

(−mgCosθ + FN) = 0 & (mgSinθ − Fs,fr) = 0

mgSinθ = Fs,fr

mgSinθ = μs⋅FN

mg = μs⋅FN ⁄ Sinθ

Fapp

Fapp

Fw

FN

Fw

FN

Fstaticfriction

Fw

70.0 kg 70.0 kg

70.0 kg

FN

Fslidingfriction

Fapp

Fapp

μsliding = 0.30

μstatic = 0.40

F fr

(N)

Fapp (N)

Fsliding = μslidingFN

Fstatic = μstaticFNmax

F static

Fstaticmax

Calculate the friction force acting on the crate when Fapp = 0, Fapp > 0 but crate does not move, and when Fapp > 0 and crate slides.

4.9 Static and Kinetic Friction

Fapp

Fapp

Lab 7 — Determining the Coefficient of FrictionAP

PHYS

θ

Fkfr = μk FN

Fw

FN

Fnet = Fw + FN = 0.

AP

PHYS

4.9 Static and Kinetic FrictionFriction has its basis in surfaces that are not completely smooth.

AP

PHYS

Friction has its basis in surfaces that are not completely smooth.

Fw

FNFappFapp

Fw + FN = 0. AND Fstatic + Fapp = 0.friction

Fstaticfriction

Fstaticfriction

4.9 Static and Kinetic Friction

AP

PHYS

Friction has its basis in surfaces that are not completely smooth.

Fw

FNFappFapp

Fw + FN = 0. AND Fstatic + Fapp = 0.friction

Fstaticfriction

Fstaticfriction

4.9 Static and Kinetic Friction

AP

PHYS

Friction has its basis in surfaces that are not completely smooth.

Fw

FN

Fw + FN = 0.

Fapp

Fslidingfriction

Fslidingfriction

Fsliding < Fapp friction

4.9 Static and Kinetic Friction

Warm Up (10/28/15) — Friction

A person has a choice of either pushing or pulling a sled at a constant velocity, as the drawing illustrates. Friction is present. If the angle θ is the same in both cases, does it require less force to push or to pull the sled?

AP

PHYS

To pull, because the upward component of the pulling force reduces the normal force and, therefore, also reduces the force of kinetic friction acting on the sled.

4.9 STATIC AND KINETIC FRICTIONAL FORCES 109

Static friction opposes the impending relative motion between two objects, while ki-

netic friction opposes the relative sliding motion that actually does occur. In either case,

relative motion is opposed. However, this opposition to relative motion does not mean that

friction prevents or works against the motion of all objects. For instance, the foot of a per-

son walking exerts a force on the earth, and the earth exerts a reaction force on the foot.

This reaction force is a static frictional force, and it opposes the impending backward mo-

tion of the foot, propelling the person forward in the process. Kinetic friction can also

cause an object to move, all the while opposing relative motion, as it does in Example 10.

In this example the kinetic frictional force acts on the sled and opposes the relative motion

of the sled and the earth. Newton’s third law indicates, however, that since the earth exerts

the kinetic frictional force on the sled, the sled must exert a reaction force on the earth. In

response, the earth accelerates, but because of the earth’s huge mass, the motion is too

slight to be noticed.

Solution Algebraically combining the results of each step, we find that

Note that the mass m of the sled and rider is algebraically eliminated from the final

result. Thus, the displacement of the sled is

Related Homework: Problems 48, 49, 85

!16 mx "vx

2 # v0x2

2(#$kg)"

(0 m/s)2 # (!4.0 m/s)

2

2[#(0.050)(9.80 m/s2)]

"

"v 2

x # v 2

0x

2!#!kFN

m ""

v 2

x # v 2

0x

2!#!kmgm "

"v 2

x # v 2

0x

2(#!kg)x "

v 2

x # v 2

0x

2ax"

v 2

x # v 2

0x

2!#fk

m "

STEP 1 STEP 2 STEP 3 STEP 4

(The answers are given at the end of the book.)

14. Suppose that the coefficients of static and kinetic friction have values such that !s "1.4 !k for a crate in contact with a cement floor. Which one of the following statements istrue? (a) The magnitude of the static frictional force is always 1.4 times the magnitude of the kinetic frictional force. (b) The magnitude of the kinetic frictional force is always 1.4 times the magnitude of the static frictional force. (c) The magnitude of the maximumstatic frictional force is 1.4 times the magnitude of the kinetic frictional force.

15. A person has a choice of either pushing or pulling a sled at a constant velocity, as thedrawing illustrates. Friction is present. If the angle is the same in both cases, does it re-quire less force to push or to pull the sled?

16. A box has a weight of 150 N and is being pulled across a horizontal floor by a forcethat has a magnitude of 110 N. The pulling force can point horizontally, or it can pointabove the horizontal at an angle When the pulling force points horizontally, the kineticfrictional force acting on the box is twice as large as when the pulling force points at theangle Find

17. A box rests on the floor of an elevator. Because of static friction, a force is required tostart the box sliding across the floor when the elevator is (a) stationary, (b) acceleratingupward, and (c) accelerating downward. Rank the forces required in these three situa-tions in ascending order—that is, smallest first.

".".

".

"

C H E C K Y O U R U N D E R S TA N D I N G!

The physics ofwalking.

!!

2762T_ch04_087-134.qxd 4/15/08 5:30 PM Page 109

Fkinetic = μ⋅FNfriction

Warm Up (10/30/15) — Friction

A box has a weight of 150 N and is being pulled across a horizontal floor by a force that has a magnitude of 110 N. The pulling force can point horizontally, or it can point above the horizontal at an angle θ. When the pulling force points horizontally, the kinetic frictional force acting on the box is twice as large as when the pulling force points at the angle θ. Find θ

AP

PHYS

4.9 STATIC AND KINETIC FRICTIONAL FORCES 109

Static friction opposes the impending relative motion between two objects, while ki-

netic friction opposes the relative sliding motion that actually does occur. In either case,

relative motion is opposed. However, this opposition to relative motion does not mean that

friction prevents or works against the motion of all objects. For instance, the foot of a per-

son walking exerts a force on the earth, and the earth exerts a reaction force on the foot.

This reaction force is a static frictional force, and it opposes the impending backward mo-

tion of the foot, propelling the person forward in the process. Kinetic friction can also

cause an object to move, all the while opposing relative motion, as it does in Example 10.

In this example the kinetic frictional force acts on the sled and opposes the relative motion

of the sled and the earth. Newton’s third law indicates, however, that since the earth exerts

the kinetic frictional force on the sled, the sled must exert a reaction force on the earth. In

response, the earth accelerates, but because of the earth’s huge mass, the motion is too

slight to be noticed.

Solution Algebraically combining the results of each step, we find that

Note that the mass m of the sled and rider is algebraically eliminated from the final

result. Thus, the displacement of the sled is

Related Homework: Problems 48, 49, 85

!16 mx "vx

2 # v0x2

2(#$kg)"

(0 m/s)2 # (!4.0 m/s)

2

2[#(0.050)(9.80 m/s2)]

"

"v 2

x # v 2

0x

2!#!kFN

m ""

v 2

x # v 2

0x

2!#!kmgm "

"v 2

x # v 2

0x

2(#!kg)x "

v 2

x # v 2

0x

2ax"

v 2

x # v 2

0x

2!#fk

m "

STEP 1 STEP 2 STEP 3 STEP 4

(The answers are given at the end of the book.)

14. Suppose that the coefficients of static and kinetic friction have values such that !s "1.4 !k for a crate in contact with a cement floor. Which one of the following statements istrue? (a) The magnitude of the static frictional force is always 1.4 times the magnitude of the kinetic frictional force. (b) The magnitude of the kinetic frictional force is always 1.4 times the magnitude of the static frictional force. (c) The magnitude of the maximumstatic frictional force is 1.4 times the magnitude of the kinetic frictional force.

15. A person has a choice of either pushing or pulling a sled at a constant velocity, as thedrawing illustrates. Friction is present. If the angle is the same in both cases, does it re-quire less force to push or to pull the sled?

16. A box has a weight of 150 N and is being pulled across a horizontal floor by a forcethat has a magnitude of 110 N. The pulling force can point horizontally, or it can pointabove the horizontal at an angle When the pulling force points horizontally, the kineticfrictional force acting on the box is twice as large as when the pulling force points at theangle Find

17. A box rests on the floor of an elevator. Because of static friction, a force is required tostart the box sliding across the floor when the elevator is (a) stationary, (b) acceleratingupward, and (c) accelerating downward. Rank the forces required in these three situa-tions in ascending order—that is, smallest first.

".".

".

"

C H E C K Y O U R U N D E R S TA N D I N G!

The physics ofwalking.

!!

2762T_ch04_087-134.qxd 4/15/08 5:30 PM Page 109

Fk,fr = μk⋅FN

Case 1= μk⋅(mg)

Case 2Fk,fr = μk⋅FN FT⋅Sinθ

mg

FN

= μk⋅(mg − FT⋅Sinθ)μk⋅(mg) =2×[ μk⋅(mg − FT⋅Sinθ)]

mg = 2mg − 2FT⋅Sinθ 2FT⋅Sinθ = mg

Sinθ = mg ⁄ 2FT

θ = Sin−1 (mg ⁄ 2FT)