1. Forces in Two Dimensions
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. Use your trigonometric functions to solve the x & y components
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. A a Vertical component of the tension of A Force of the boom
Horiz. component
of the tension of A
Weight

10. W FH FV opposing W is The vertical comp. TA FT of A FBoom
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. Calculate the pulling force required to accelerate the sled
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 = kg
mk = 0.200
< a = 53.0o
Calculate: abox a

27. Box = 250 kg
ms = 0.40 mk = 0.20
Calculate: < a required to set the box in motion & abox a

28. Box = kg
ms = 0.50 mk = 0.30
Calculate: < 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 = kg
mk = 0.20
< 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 TA TB
Identify all forces W

32. W A B a Vertical Component Vertical Of TB Component Of Ta Horizontal

33. Fnet = 0 W = mg A B TAcosa + TBcosb = 0 TAsina + TBsinb + W = 0 a

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
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 C Wx + WY FV of C a b FV of A FV of B + FV of C FH of A FH of C
FH of B C
FH of C
Wx +
FV of C WY

40. A B C Wx + WY FV of C a b FV of A FV of B FH of A FH of C FH of B

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 = 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
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 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 W
Calculate: abox