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Chapter 7.1

- Forces in Two Dimensions

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.

a

A

B

W 2,000.0 N a 53o Calculate TA TB

W

2-D Forces

- Solve the force in each dimension independently

2-D Forces

- Use your trigonometric functions to solve the x

y components

2-D Forces

- x y components could be the vertical force (FV)

or the horizontal force (FH)

2-D Forces

- x y components could be the vertical force

(F) or the horizontal force (F?)

A

a

W

Identify all forces

Vertical component of the tension of A

A

a

Force of the boom

Horiz. component of the tension of A

Weight

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

A

a 37o

a

250 kg

Calculate TA of line A force of the boom

A

a 45o

a

500.0 N

Calculate FT of line A force of the boom

A

a 53o

a

200.0 kg

Calculate FT of line A force of the boom

a

A

B

W 2,000.0 N a 37o Calculate TA TB

W

W 2500 N A 53o Calculate FBoom

W

a

FA 100 lbs a 10o Calculate TB FH

FA

B

a

a

a 37o Wsled 250 N

ms 0.1 Calculate the pulling force required to

accelerate the sled

a

a 37o mmower 100.0 kg

mk 0.25 Calculate the force required to push

the mower at constant v

a

a 37o mmower 20.0 kg

mk 0.20 Calculate amower When the person Pushes

with 50.0 N

a

Determine the forces acting on the box

Ff

FN

F

F?

W

a

Ff

FN

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

a

F?

F

W

a

Box 1500 kg a 30o Calculate F, F?, Ff if v

is constant, m

a

Box 2500 kg a 37o Calculate F, F?, Ff if a

2.0 m/s2, m

a

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

a

Box 100.0 kg mk 0.200 lt a 53.0o

Calculate abox

a

Box 250 kg ms 0.40 mk 0.20 Calculate lt a

required to set the box in motion

abox

a

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

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

a

b

A

B

Identify all forces

W mg

a

b

TB

TA

Identify all forces

W

a

b

Vertical Component Of TB

A

Vertical Component Of Ta

B

Horizontal Component Of TA

Horizontal Component Of TB

W

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

a

b

A

a 37o b 53o

B

Calculate the tension of both A B

50.0 kg

Calculate the force required to accelerate a 9800

N sled at 3.0 m/s2 when the kinetic frictional

coefficient is 0.50

a

b

A

a 30o b 53o

B

Calculate the tension of both A B

25 kg

a

b

A

a 37o b 53o

B

Calculate the tension of both A B

2.5 kg

a

b

A

B

- a 37o
- 53o
- Y 1.00 kN

C

X

Y

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

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

A 20.0 kg block is sliding down a board that is

30o from horizontal at a constant speed.

Calculate the frictional coefficient.

Box 100.0 kg a 25o Calculate F, F?, Ff if

v is constant, m

Calculate tan a

a

Box 50.0 kg a 53o Calculate F, F?, Ff if v

is constant, m

Calculate tan a

a

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

Calculate tan a

a

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

Calculate tan a

a

A

a

250 kg

Calculate the tension Of A if a 45o

a

b

A

a 37o b 53o

B

Calculate the tension of both A B

2.5 kg

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.

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.

- 36.87o
- W 294 N
- m 0.100

38.0 N

a

Calculate abox

W