Chapter N6

Linearly Constrained MotionN6B.1, B.4, B.5, S.1, S.8Due Monday

Forces from motion

Implies

Three equations

amFnet

zznet

yynet

xxnet

z

y

x

znet

ynet

xnet

maF

maF

maF

a

a

a

m

F

F

F

,

,

,

,

,

,

Ex. What force is required to push a 50 kg cart with frictionless wheels up a 30 degree incline at constant speed?

How much more force is required to push a cart up an incline at constant speed than to hold it still?

The same force is required for both Draw the free body diagram for the cart. Draw the net force diagram for the cart. Do the trig and write the acceleration

equation(s).amFnet

Solution As there is no acceleration, the sum of the

forces is zero.

0

00

0

cos

0

sin

0

0

0 Hand

N

F

Fmg

mg

θθ

mgmg cosθ

mg sinθFHand=245 N

Friction forces

For static friction Ff=μsN This is what is necessary to “break the

object loose” and get it moving For kinetic friction Ff=μkN

This is what is necessary to keep it moving.

The static friction is usually significantly higher than the kinetic friction.

Ex. What force is required to push a 50 kg cart with a μk of .3 up a 30 degree incline at constant speed?

This problem is the same as we solved before except that we need to include Ff.

Write the vector equation on your paper.

0

00

0

cos

0

cossin

0

0

0 Hand

N

k F

Fmg

mgmg

FHand=245 N + 127.3 N = 372.3 N

Drag forces The drag force of an object moving with a

velocity v, through a fluid of density ρ, and cross-sectional area A is given by

Where C is a constant determined by the shape of the object. ( for a sphere C = .5)

2

2

1AvCFD

Find the terminal velocity of a baseball in the atmosphere if it is dropped from a hovering helicopter

2

2

1AvCFD

C = 0.5

ρ = 1.29 kg/m3

Radius = 7 cm

A = π(.07 m)2 = .0154 m2

Mass of ball = .14 kg

Terminal velocity of the ball = 16.8 m/s

Find the acceleration of a 50 kg cart with frictionless wheels rolling down a 30 degree incline.

Draw a free body diagram Draw a net force diagram Write the vector equations in column

vector form

0

00

0

cos

0

cossin

0

0

0 Hand

N

k F

Fmg

mgmg

a = 2.35 m/s2

Find the acceleration of a cart with frictionless wheels rolling down a 30 degree incline.

0

0

0

0

0

cos

0

sin

0

0

NFmg

mgma

In this case

ma=mgsinθ

a=gsinθ

a=9.8m/s2·sin(30º)=4.9m/s2

Find the acceleration of a 50 kg cart with coefficient of kinetic friction of 0.3 sliding down a 30 degree incline.

Draw a free body diagram Draw a net force diagram Write the vector equations in matrix

0

00

0

cos

0

cossin

0

0

0 F

Fmg

mgmg

N

k

cossin mgmgmaF k

cossin gga k a=2.35 m/s2

Problems chapter N6

N6B.1, B.4, B.5, S.1, S.8 Due Monday