2-D Force Problems

7 kg2N

3N

8N

Find the direction and magnitude of the acceleration of the box.

Sally pushes an old fashioned lawnmower at a constant speed of 3 m/s. She pushes with 100 N at an angle of 65°.

Draw a FBD and find the vertical and horizontal components of her push.

How much friction must there be?

Find the horizontal force on the box.

NO FRICTION

Draw FBD

Find the vertical component of the pull of the rope.

If the box has a mass of 8 kg

Find its acceleration

Find its weight Find the normal force that the ground pushes up.

Two dimensional forces must be summed up in the x direction alone, the y direction alone, then finally connected head to tail and added with the pythagorean theorem

Adding Multiple Forces that are not at right angles

2 Possible Strategies:

Graphical method:

1. Draw the vectors to scale.

2. Connect the vectors head to tail.

3. Resultant goes from head of first to the tail of the last.

Analytical method:

1. Use trigonometry to resolve all vectors into X and y components.

2. Add all the x vectors to each other., then add all the y vectors to each other.

3. Find the resultant with the Pythagorean Theorem.

These three cartoon creatures are trying to pull a statue. Graphically find the resultant vector if:

The Ant applies 100N@2200

The Penguin 200N@2400

Jackie Chan 300N@3080

Which vector is which?

Will it move, and which way

will it go ?

0

90

180

270

For graphical vector addition to work, the arrows must be drawn at exactly the right angle using a protractor and must be drawn to scale (proportionally) using a ruler. Check this drawing with a ruler and protractor

The Ant applies 100N@220

The Penguin 200N@240

Jackie Chan 300N@308

200N

300N

100N

R=240N@2700

Combining the vectors “tip to tail”, regardless of the order, gives us the resultant.

How can we graphically find how big this resultant is?