Forces in Two Dimensions

1
Chapter 7.1

• Forces in Two Dimensions

2
2-D Forces

• Solve the force in each dimension independently

3
2-D Forces

• Use your trigonometric functions to solve the x
  y components

4
2-D Forces

• x y components could be the vertical force (FV)
  or the horizontal force (FH)

5
2-D Forces

• x y components could be the vertical force
  (F) or the horizontal force (F?)

6
A
a
W
Identify all forces
7
Vertical component of the tension of A
A
a
Force of the boom
Horiz. component of the tension of A
Weight
8
FH
FV opposing W is The vertical comp.
TA
FT of A
FBoom
a
FH the horizontal comp. which opposes the boom
W
FV -W TA sin a FH TA cos a
9
A
a 37o
a
250 kg
Calculate FT of line A force of the boom
10
A
a 45o
a
500.0 N
Calculate FT of line A force of the boom
11
A
a 53o
a
200.0 kg
Calculate FT of line A force of the boom
12
a
A
B
W 2,000.0 N a 37o Calculate TA TB
W
13
W 2500 N A 53o Calculate FBoom
W
a
14
FA 100 lbs a 10o Calculate TB FH
FA
B
a
a
15
Determine the forces acting on the box
16
Ff
FN
F
F?
W
a
17
Ff
FN

• F W sin a
• F? W cos a
• FN - F?
• Ff mFN

a
F?
F
W
a
18
Box 1500 kg a 30o Calculate F, F?, Ff if v
is constant, m
a
19
Box 2500 kg a 37o Calculate F, F?, Ff if a
2.0 m/s2, m
a
20

• Box 2500 kg
• m 0.20
• 37o
• Calculate
• F, F?,
• Ff, a

a
21
Box 200.0 kg ms 0.50 mk 0.30 Calculate lt a
required to set the box in motion
abox
If the ramp in 50.0 m long, calculate the vf
of the box
a
22
Box 250 kg ms 0.40 mk 0.20 Calculate lt a
required to set the box in motion
abox
a
23
Box 100.0 kg mk 0.20 lt a 53o
Calculate abox
a
24
Box 100.0 kg mk 0.20 lt a 37o
Calculate the force required to accelerate the
box up the plane at 2.0 m/s2
a
25
a 37o Wsled 250 N
ms 0.1 Calculate the pulling force required to
accelerate the sled
a
26
a 37o Wsled 100 N
mk 0.25 Calculate the force required to push
the mower at constant v
a
27
a 37o Wsled 100 N
mk 0.40 Calculate the force required to push
the mower at constant v
a
28
a
b
A
B
Identify all forces
W mg
29
a
b
TB
TA
Identify all forces
W
30
a
b
Vertical Component Of TB
A
Vertical Component Of Ta
B
Horizontal Component Of TA
Horizontal Component Of TB
W
31
a
b
A
B
TB sin b
TA sin a
b
a
Ta cos a
TB cos b
Fnet 0 TAcosa TBcosb 0 TAsina TBsinb W
0
W mg
32
a
b
A
a 37o b 53o
B
Calculate the tension of both A B
50.0 kg
33
Calculate the force required to accelerate a 9800
N sled at 3.0 m/s2 when the kinetic frictional
coefficient is 0.50
34
a
b
A
a 30o b 53o
B
Calculate the tension of both A B
25 kg
35
a
b
A
a 37o b 53o
B
Calculate the tension of both A B
2.5 kg
36
a
b
A
B

• a 37o
• 53o
• Y 1.00 kN

C
X
Y
37
a
b
FV of A
FV of B FV of C
A
B
FH of A
FH of C
FH of B
C
FH of C
Wx FV of C
WY
38
a
b
A
B
FV of A
FV of B
FH of C
FH of A
C
FH of B
FH of C
FV of C
FV of C
Wx FV of C
WY
39
A 20.0 kg block is sliding down a board that is
30o from horizontal at a constant speed.
Calculate the frictional coefficient.
40
Box 1500 kg a 25o Calculate F, F?, Ff if v
is constant, m
Calculate tan a
a
41
Box 50.0 kg a 53o Calculate F, F?, Ff if v
is constant, m
Calculate tan a
a
42

• Box 10.0 kg
• 37o
• a 2.0 m/s2 down Calculate F,
• F?, Ff,
• , m

Calculate tan a
a
43

• Box 1.0 kg
• 45o, m 0.20
• a 2.0 m/s2 up Calculate F,
• F?, Ff,
• FA, m

Calculate tan a
a
44
A
a
250 kg
Calculate the tension Of A if a 45o
45
a
b
A
a 37o b 53o
B
Calculate the tension of both A B
2.5 kg
46
A 50.0 N force is applied to a rope attached to
one end of a 5.0 m sled at a 37o angle from
horizontal. Calculate FH, FV, the torque on the
sled.
47
A 500.0 kg box slides down an inclined plane that
is 53o from horizontal with an acceleration of
3.0 m/s2. Calculate F, F?, Fnet, Ff, m.