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
Drill
Calculate the apparent weight of a 50.0 kg man
acceleration upwards in an elevator at 3.0 m/s2.
4
a
A
B
W 2,000.0 N a 53o Calculate TA TB
W
5
2-D Forces

• Solve the force in each dimension independently

6
2-D Forces

• Use your trigonometric functions to solve the x
  y components

7
2-D Forces

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

8
2-D Forces

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

9
Drill

• Calculate the frictional coefficient acting on a
  10.0 kg box sliding when a 39.8 N force causes an
  acceleration of 3.00 m/s2.

10
A
a
W
Identify all forces
11
Vertical component of the tension of A
A
a
Force of the boom
Horiz. component of the tension of A
Weight
12
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
13
A
a 37o
a
250 kg
Calculate TA of line A force of the boom
14
A
a 53o
a
200.0 kg
Calculate FT of line A force of the boom
15
a
A
B
W 2,000.0 N a 37o Calculate TA TB
W
16
W 2500 N A 53o Calculate FBoom
W
a
17
A
a 45o
a
500.0 N
Calculate FT of line A force of the boom
18
FA 100 lbs a 10o Calculate TB FH
FA
B
a
a
19
a 37o Wsled 250 N
ms 0.1 Calculate the pulling force required to
accelerate the sled
a
20
a 37o mmower 100.0 kg
mk 0.25 Calculate the force required to push
the mower at constant v
a
21
a 37o mmower 20.0 kg
mk 0.20 Calculate amower When the person Pushes
with 50.0 N
a
22
Determine draw FBDs of the forces acting on
the box
23
Ff
FN
F
F?
W
a
24
Ff
FN

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

a
F?
F
W
a
25
Box 1500 kg a 30o Calculate F, F?, Ff if v
is constant, m
a
26
Box 2500 kg a 37o Calculate F, F?, Ff if a
2.0 m/s2, m
a
27

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

q
28
Box 100.0 kg mk 0.200 lt q 53.0o
Calculate abox
q
29
Box 10.0 kg ms 0.40 mk 0.20 Calculate ? q
required to set the box in motion
abox
q
30
Box 100.0 kg mk 0.20 lt q 37o
Calculate the force required to accelerate the
box up the plane at 2.0 m/s2
q
31
a
b
A
B
Identify all forces
W mg
32
a
b
TB
TA
Identify all forces
W
33
a
b
Vertical Component Of TB
A
Vertical Component Of Ta
B
Horizontal Component Of TA
Horizontal Component Of TB
W
34
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
35
a
b
A
a 37o b 53o
B
Calculate the tension of both A B
50.0 kg
36
Calculate the force required to accelerate a 9800
N sled at 3.0 m/s2 when the kinetic frictional
coefficient is 0.50
37
a
b
A
a 30o b 53o
B
Calculate the tension of both A B
25 kg
38
a
b
A
a 37o b 53o
B
Calculate the tension of both A B
10.0 kg
39
Box 2.0 kg ms 0.50 mk 0.30 Calculate ? q
required to set the box in motion
abox
If the box slides 50.0 m, calculate the vf of
the box
q
40
a
b
A
B

• a 37o
• 53o
• Y 1.00 kN

C
X
Y
41
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
42
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
43
A 20.0 kg block is sliding down a board that is
30o from horizontal at a constant speed.
Calculate the frictional coefficient.
44
Box 100.0 kg q 25o Calculate F, F?, Ff if
v is constant, m
Calculate tan a
q
45
Box 50.0 kg q 53o Calculate F, F?, Ff if v
is constant, m
Calculate tan a
q
46

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

Calculate tan a
q
47

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

Calculate tan a
q
48
A
q
250 kg
Calculate the tension Of A if q 45o
49
a
b
A
a 37o b 53o
B
Calculate the tension of both A B
2.5 kg
50
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.
51
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.
52
q 36.87o W 294 N m 0.100
38.0 N
q
Calculate abox
W