Forces in Two Dimensions

1
Chapter 7.1

• Forces in Two Dimensions

2
Drill

• Calculate the frictional coefficient acting on a
  10.0 kg box sliding when a 50 N force causes an
  acceleration of 3.00 m/s2.

3
a
A
B
W 2,000.0 N a 53o Calculate TA TB
W
4
2-D Forces

• Solve the force in each dimension independently

5
2-D Forces

• Use your trigonometric functions to solve the x
  y components

6
2-D Forces

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

7
2-D Forces

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

8
A
a
W
Identify all forces
9
Vertical component of the tension of A
A
a
Force of the boom
Horiz. component of the tension of A
Weight
10
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
11
A
a 37o
a
250 kg
Calculate TA of line A force of the boom
12
A
a 45o
a
500.0 N
Calculate FT of line A force of the boom
13
A
a 53o
a
200.0 kg
Calculate FT of line A force of the boom
14
a
A
B
W 2,000.0 N a 37o Calculate TA TB
W
15
W 2500 N A 53o Calculate FBoom
W
a
16
FA 100 lbs a 10o Calculate TB FH
FA
B
a
a
17
a 37o Wsled 250 N
ms 0.1 Calculate the pulling force required to
accelerate the sled
a
18
a 37o mmower 100.0 kg
mk 0.25 Calculate the force required to push
the mower at constant v
a
19
a 37o mmower 20.0 kg
mk 0.20 Calculate amower When the person Pushes
with 50.0 N
a
20
Determine the forces acting on the box
21
Ff
FN
F
F?
W
a
22
Ff
FN

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

a
F?
F
W
a
23
Box 1500 kg a 30o Calculate F, F?, Ff if v
is constant, m
a
24
Box 2500 kg a 37o Calculate F, F?, Ff if a
2.0 m/s2, m
a
25

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

a
26
Box 100.0 kg mk 0.200 lt a 53.0o
Calculate abox
a
27
Box 250 kg ms 0.40 mk 0.20 Calculate lt a
required to set the box in motion
abox
a
28
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
29
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
30
a
b
A
B
Identify all forces
W mg
31
a
b
TB
TA
Identify all forces
W
32
a
b
Vertical Component Of TB
A
Vertical Component Of Ta
B
Horizontal Component Of TA
Horizontal Component Of TB
W
33
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
34
a
b
A
a 37o b 53o
B
Calculate the tension of both A B
50.0 kg
35
Calculate the force required to accelerate a 9800
N sled at 3.0 m/s2 when the kinetic frictional
coefficient is 0.50
36
a
b
A
a 30o b 53o
B
Calculate the tension of both A B
25 kg
37
a
b
A
a 37o b 53o
B
Calculate the tension of both A B
2.5 kg
38
a
b
A
B

• a 37o
• 53o
• Y 1.00 kN

C
X
Y
39
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
40
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
41
A 20.0 kg block is sliding down a board that is
30o from horizontal at a constant speed.
Calculate the frictional coefficient.
42
Box 100.0 kg a 25o Calculate F, F?, Ff if
v is constant, m
Calculate tan a
a
43
Box 50.0 kg a 53o Calculate F, F?, Ff if v
is constant, m
Calculate tan a
a
44

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

Calculate tan a
a
45

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

Calculate tan a
a
46
A
a
250 kg
Calculate the tension Of A if a 45o
47
a
b
A
a 37o b 53o
B
Calculate the tension of both A B
2.5 kg
48
A 50.0 N force is applied to a rope attached to
one end of a 40.0 kg sled at a 37o angle from
horizontal. Calculate FH, FV, the acceleration
of the sled if m 0.10.
49
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.
50

• 36.87o
• W 294 N
• m 0.100

38.0 N
a
Calculate abox
W