Unit 6 Review for Test

SOLUTIONS

Lyzinski Physics

1. Draw out the full RUBBER STAMP that we start EVERY

incline plane problem with.

W

W||

W

||

FN

2. A 4 kg block is sitting at rest on a 30o inclined plane.

Find the minimum coefficient of static friction that will keep the

block at rest. (TWO answers are expected: one should contain

only variables, and one should be a rounded number).

FN

Wperp

W||

Ff

577.)30tan(tancos

sin

cossin

)0(

coscos

cossin

||

||

||

mg

mg

mgmg

FW

mFWmaF

mgFFmgWF

mgWmgWmgW

f

fNet

NfN

3. A 5 kg block is sitting on the frictionless inclined plane shown below.

A 20 kg weight is draped over the pulley and attached to the 5 kg

block via a cable. Find:

a) the acceleration of the system.

b) the tension in the rope.

c) the time that it will require for the block on the incline to travel

.5 m, assuming that it starts at rest.

50o

520

234.6254.29196

s

maa

MaFNet

5 20 20(9.8) = 196N 5(9.8)sin(50)

= 37.54N

a

(Continued on next)

3. A 5 kg block is sitting on the frictionless inclined plane shown below.

A 20 kg weight is draped over the pulley and attached to the 5 kg

block via a cable. Find:

a) the acceleration of the system.

b) the tension in the rope.

c) the time that it will require for the block on the incline to travel

.5 m, assuming that it starts at rest.

sec4.get

oHarrison tMarvin Use

??

34.6

5.

0

2

1

t

t

s

ma

md

V

50o

520

20 a

T

20(9.8) = 196N

NTTN

maFNet

2.69)34.6(20196

4. For the Atwood Machine at the right, find:

a) the acceleration of the system.

b) the tension in the rope.

288.5

58.92.39

s

ma

amaFNet

4 kg

1 kg

4 14(9.8) = 39.2N 1(9.8) = 9.8N

a

439.2N T

a

NT

TmaFNet

68.15

)88.5(42.39

5. A box of mass m is being pushed up a o incline by a force of F.

The coefficient of kinetic friction between the block and the

incline is . Find the acceleration of the block, assuming that the

block does indeed move up the incline. (note: your answer

should contain only variables).

m

mgmgFa

mamgmgF

maWFFmaF

mgFFmgWF

mgWmgWmgW

push

push

fpushNet

NfN

sincos

sincos

coscos

cossin

||

||

FN

Wperp

W||

Ff

Fpush

6. A 60 kg man is riding on an elevator while standing on a scale. A

50 kg chandelier is hanging from a metal wire in the ceiling

above the man’s head. Find:

a) the apparent weight of the man when the elevator is moving

upward with a constant acceleration of 3 m/s2.

NF

NmgmaWmaF

maWF

maF

N

N

N

net

768eight Apparent W

768)8.93(60

W=mg

FN = apparent weight

a

6. A 60 kg man is riding on an elevator while standing on a scale.

A 50 kg chandelier is hanging from a metal wire in the ceiling

above the man’s head. Find:

b) the tension in the chandelier wire when the elevator is

accelerating downward at a constant acceleration of 2 m/s2.

NmamgmaWT

maTW

maFnet

390)28.9(50

W=mg

T

a

chandelier

6. A 60 kg man is riding on an elevator while standing on a scale.

A 50 kg chandelier is hanging from a metal wire in the ceiling

above the man’s head. Find:

b) the minimum upward acceleration that the elevator must

constantly move at in order to snap the chandelier wire (which

is capable of withstanding 1000N of force).

2

2

2.10

)8.9(501000

)(

s

m

s

m

net

a

akgN

gammgmaWmaT

maWT

maF

W=mg

T

a

chandelier

7. A man on skis stands at the top of a inclined hill. He begins to

descend. If the hill’s incline angle is 35o, and if the man travels

200 m down the hill in 10 sec, find the coefficient of friction

between the man’s skis and the snow. You may assume that

the man doesn’t push off with his ski poles, but rather simply

2.0)35cos()8.9(

4)35sin()8.9(

cos

sin

cossin

cossin

coscos

cossin

40sec,10,200

||

||

1 2

g

ag

agg

mamgmg

maFWmaF

mgFFmgWF

mgWmgWmgW

avtmd

fNet

NfN

s

m

FN

Wperp

W||

Ff

moves downhill due to the effects of gravity.

a

8. Find the minimum angle needed to force a 50 kg block to slide down

an incline with a static frictional coefficient of 0.5.

o

o

f

NfN

mg

mg

mgmg

FW

mgFFmgWF

mgWmgWmgW

56.26

56.26)5(.tan)(tantan

cos

sin

cossin

on,acceleratian induce To

coscos

cossin

11

||

||

FN

Wperp

W||

Ff

a

9. You weigh 600N and you are sitting in a space ship that blasts off.

The acceleration of the spaceship is 20 m/s2 upward.

a) Find the “apparent weight” that you will feel, in Newtons.

b) Find the “apparent weight” that you will feel, in g’s.

sg' 04.3600/356.824,1 sg' of #

356.824,1)8.920)(22.61(

)(

22.61600

NN

N

gammgmaF

mamgF

maF

kgmNmgW

N

N

net

W=mg

FN = apparent weight

a

person

10. The system below uses rope that can withstand a

maximum tension of 35 0N. If the coefficient of

friction between the block and the table is 0.3, will the

rope snap or not? Make sure to fully explain your

answer.

2058.2

1002.88196490

s

ma

amaFNet

20 5020(9.8) = 196N 50(9.8) = 490N

a

30 kg

50

kg20

kg

30

Ff = (0.3)(30)(9.8) = 88.2N

(continued on next slide)

10. The system below uses rope that can withstand a

maximum tension of 35 0N. If the coefficient of

friction between the block and the table is 0.3, will the

rope snap or not? Make sure to fully explain your

answer.

20 5020(9.8) = 196N 50(9.8) = 490N

a

50T 490N

a

!!!!!!!1.387

)058.2(50490

SNAPNT

TmaFNet

30 kg

50

kg20

kg

30

Ff = (0.3)(30)(9.8) = 88.2NCUT THE ROPE!!!!

11. What coefficient of friction would be necessary to avoid a rope

“snappage” in problem #10?

30 kg

50

kg20

kg

Work backwards

50T 490N

a

2

max

8.250350490

350

50490

s

maaNN

NT

aTNmaFNet

(continued on next slide)

11. What coefficient of friction would be necessary to avoid a rope

“snappage” in problem #10?

30 kg

50

kg20

kg

Work backwards

20 5020(9.8) = 196N 50(9.8) = 490N

047.)8.9)(30(

)8.2(100196490

)8.9)(30()8.2(100196490

)8.2(100)8.9)(30(196490

maFNet

30

Ff = ()(30)(9.8)From

previous slide

12. Find the angle necessary to keep the system below at rest,

assuming that both inclines are frictionless.

20 50W||

o6.48)8.9(20

30sin)8.9(30sin

)8.9(20

30sin)8.9(30sin

30sin)8.9(30sin)8.9(20

1

20kg 30kg

30o

20 5020(9.8)sin

W||

20(9.8)sin(30)

13. An Atwood machine has two blocks, of masses “m” and “M” respectively (where

M > m), being held at a height of “h” above the table top. The blocks are suddenly

released. Find …

a) the acceleration of the system in terms of “m”, “M”, and “g”.

b) the tension of the system in terms of “m”, “M”, and “g”.

c) the maximum height above the table that the less massive block will reach if

m = 5 kg, M = 12 kg, and h = 20 cm.

mM

gmMa

amMmgMg

)(

)(

m Mm Mmg Mg

a

M

Mg

T

a

cmcmcmcmH

myyyavv

vvahvv

mM

gmMa

sm

s

m

2.482.82020

082.)8.9(227.102

27.1)2)(.035.4(22

035.4512

)8.9)(512()(

22

1

2

2

2

2

2

2

1

2

2

2

h

mM

gmMMMgT

MaMgT

MaTMg

)(

14. A block of mass “m” is placed on an incline whose angle of

inclination is “q”. If the block slides down the incline, and if the

coefficient of kinetic friction is “m”, find the acceleration of the

block in terms of m, , , and/or g.

agg

mamgmg

maFWmaF

mgFFmgWF

mgWmgWmgW

fNet

NfN

cossin

cossin

coscos

cossin

||

||FN

Wperp

W||

Ff

a

15) The 10 kg block below is being pushed up the incline by a constant force of 150

Newtons. If the coefficient of kinetic friction on the incline is 0.2, find the …

a) normal force acting on the block.

b) speed that the block will attain after a 5 second push, assuming that

it starts at rest.

2

2

269.38)5(654.7)0(

654.7

10)918.110)(2(.)30sin()8.9)(20()10cos(150

sincos

918.110)10sin(150)30cos(*8.9*10

sincos

12 s

m

s

m

N

N

atvv

a

a

maFmgF

N

FmgF

FN

Wperp

W||

Ff

30o

a

10o

F

Fsin() Fcos()

16) Two blocks (each of mass 70 kg) are connected together by a light string. They are

accelerated upward by a pulling force of 2000 Newtons. Find the tension in the

string while they are being pulled upward, assuming that they are both lifted off the

ground.

2486.4

14070702000

s

ma

agg

70

kg

70

kg

70g

70g

2000N

a

70

kg

70g

T

a

NT

gT

1000

)486.4(7070

17) A military helicopter has a rope attached to the bottom of it, which is attached to a

platform on which a Hummer is sitting. The Hummer and the platform are resting

on a scale. The helicopter accelerates upward at a rate of 2.0 m/s2, and the rope

(which can handle a maximum tension of 30,000 Newtons) snaps at the exact

moment that the scale reads 1000N. Find the joint mass of the hummer and the

platform.

kgM

M

MM

MMF

12.627,2

8.11000,31

)2()8.9(000,30000,1

)2()8.9(1000

M

Mg

T

a = 2

1000N