Force Vector Sample Problems
Force Vector Sample Problems
1. What is the tension in the rope?
Sketch
20o
92.3 N Weight pulls down
Cable pulls up 92.3 N
Pushes on wall
What directions does the cable pull?
Up and to the left
Why is the vertically upward force equal to the weight?
The light is static
Math• Tension is found in the chain which makes up the
hypotenuse of the triangle.
• The opposite side is equal to the weight
(since it is directed down).
• You know the angle and the opposite side.
• Use sine (sin 𝜃 =𝑜𝑝𝑝
ℎ𝑦𝑝)
opphyp
sin
92.3 92.3hyp
sin20 .342
Tension = 270 N
2. What is the tension in the rope?
Sketch
46.15
46.15
Sketch
35o
½ of the weight pulling down. 46.15 N
½ of the weight pulled up by the cable. 46.15 N
You only need ½ of the diagram.
Why?Both sides are equal
Math
• Tension is found in the chain which makes up
the hypotenuse of the triangle.
• The opposite side is equal to the ½ weight
because there are two ropes supporting the
sign.
• You know the angle and the opposite side.
• Use the Sine function to find the hypotenuse
oppositeSin =
Hypotenuse
46.2 46.15Hyp =
sin35 .574
Tension = 80.5 N (in each cable)
3. If the roller has a mass of 65.5 kg and is being pushed with a
force of 25 N so that it moves at a constant velocity, what is the
friction force?
Horizontal Component of applied Force
Force of friction opposes horizontal force applied
Vertical Component of Force Applied + Weight of roller
Man pushes on lawn mower
Label the Sketch
65̊
Friction Force
Math• Not all of the applied force (25 N) is going into
horizontal motion because it is applied at an
angle.
• Since the roller is moving horizontally at a
constant velocity, the friction force is equal to
the applied force in the horizontal direction.
• You are looking for the adjacent side and you
know the angle and the hypotenuse
adjcos
hyp
Adj Hyp (cos ) 25 (cos 65)
Friction force = 10.6 N
One more problem
The tension in each cable of Flavor Flav’swatch is 1.5 N
They are at an angle of 70o how much does his watch weigh?
70 70
1.5 N 1.5 N
Sketch
70o
Weight of the watch
Cable with a tension of 1.5 N Cable with a tension of 1.5 N
½ the weight of the watch
½ the weight of the watch
Math
• Each chain is identical and you can find ½ of weight by finding the vertical component of one side and multiplying your answer by 2.
• Use sin function to solve for the vertical component.
oppsin
hyp
opp hyp(sin ) = 1.5 (sin70)= 1.5 (.940)= 1.41 N
Weight = 1.41 x 2
Weight = 2.82 N
Now work on Worksheet A
NOW!
Answers to Worksheet A
A.) Moving forward: Pushing downward1. 6.93 N
2. 4 N
B.) pushing against the wall: pushing up the wall
1. 1.29 N
2. 4.83 N
C.)
1. 446 N
2. down
3. 0
4. up: left
5.
6. hypotenuse
7. opposite
8. SIN
9. more
10. 892 N