Force Vector Sample Problems - North Hunterdon-Voorhees ...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,

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