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
Top Related