Lesson 1 a-f
A
To find vectors in a parallelogram use the following steps:
- Projectile movement- the only force acting is gravity
- Projectile has a single force that acts upon it
- A force is not required to keep an object in motion
- A force is only required to maintain an acceleration. And in the case of a projectile that is moving upward, there is a downward force and a downward acceleration. That is, the object is moving upward and slowing down.
- Inertia- acceleration of gravity
- Force of gravity acts upon it --> downward acceleration
- Can use Pythagorean theorem to find missing sides in vectors and find final distances
- For direction, first the direction the side you want to find is going, then the way the vector it is attached to is going.
- use soh/cah/toa to find missing angles
- Resultant is the sum of two vectors
- When displacement vectors are added, the result is a resultant displacement.
- Any vectors can be added as long as long as they have the same vector quantity
- Each part of a two dimensional vector is known as a component
- Angled vectors have two components
- Example is hanging pictures
- To solve make a triangle
To find vectors in a parallelogram use the following steps:
- Select a scale and accurately draw the vector to scale in the indicated direction.
- Sketch a parallelogram around the vector: beginning at the tail of the vector, sketch vertical and horizontal lines; then sketch horizontal and vertical lines at the head of the vector; the sketched lines will meet to form a rectangle (a special case of a parallelogram).
- Draw the components of the vector. The components are the sides of the parallelogram. The tail of the components start at the tail of the vector and stretches along the axes to the nearest corner of the parallelogram. Be sure to place arrowheads on these components to indicate their direction (up, down, left, right).
- Meaningfully label the components of the vectors with symbols to indicate which component represents which side. A northward force component might be labeled Fnorth. A rightward velocity component might be labeled vx; etc.
- Measure the length of the sides of the parallelogram and use the scale to determine the magnitude of the components in real units. Label the magnitude on the diagram.
- Construct a rough sketch (no scale needed) of the vector in the indicated direction. Label its magnitude and the angle that it makes with the horizontal.
- Draw a rectangle about the vector such that the vector is the diagonal of the rectangle. Beginning at the tail of the vector, sketch vertical and horizontal lines. Then sketch horizontal and vertical lines at the head of the vector. The sketched lines will meet to form a rectangle.
- Draw the components of the vector. The components are the sides of the rectangle. The tail of each component begins at the tail of the vector and stretches along the axes to the nearest corner of the rectangle. Be sure to place arrowheads on these components to indicate their direction (up, down, left, right).
- Meaningfully label the components of the vectors with symbols to indicate which component represents which side. A northward force component might be labeled Fnorth. A rightward force velocity component might be labeled vx; etc.
- To determine the length of the side opposite the indicated angle, use the sine function. Substitute the magnitude of the vector for the length of the hypotenuse. Use some algebra to solve the equation for the length of the side opposite the indicated angle.
- Repeat the above step using the cosine function to determine the length of the side adjacent to the indicated angle.
- If vectors are in the same direction add them and them
- After they are together, use the normal steps to find the hypotenuse
- *make sure to use soh/cah/toa