Structures and Forces

Define Vector:

a quantity having direction as well as magnitude (how big something is). Examples of vectors are acceleration and velocity.

Define Scalar:

A quantity that has only a magnitude. Examples of scalars are volume, density, speed, energy, mass, and time.

How to Draw forces on a Diagram:

How to apply vector diagrams to test whether forces are balanced or produce a Resultant

Vector diagrams are used when two forces and an angle are given. These vector diagrams are used when you need to find the resultant force of the two forces.

Apply vector diagrams to estimate the size and direction of resultant forces

Method of finding resultant forces with vector diagrams:

First, draw the object on the free body diagram (this object can be represented using a dot or a circle).

Draw the first line from the object which will be the first force. Remember to scale the forces to the distance on the diagram (1cm = 1N).

Measure the angle given(with a protractor) from the first line in order to be able to draw the second line.

After, draw the second line on the diagram and remember to scale the size of the line.

Now a parallelogram should be drawn from the two different lengths.

After the parallelogram has been drawn, a line should be drawn from the object to the other side of the parallelogram. This will give us the vector

Finally, measure the length of the vector to get the resultant force. If the direction of the resultant force wants to be measured, measure the angles on both of the sides of the vector.

Use vector diagrams to solve multiple force problems and calculate the resultant force

Follow the method above to understand the process of how to find the resultant force. Down below are free body diagrams of the process

Step 1:

Look at your Question. Draw the lines for both the forces and draw the angle separating the two forces

Step 2:

Finish the parallelogram

Step 3:

Draw the center vector and calculate its length through Pythagoras or just measuring. Also, measure the angles on both sides of the vector

Describe the direction the frictional force acts as f

Friction is a force between two surfaces that are sliding, or trying to slide, across each other. Friction always works in the direction opposite to the direction in which the object is moving or trying to move.

Explain with vectors how to arrive at a net force of zero in 1 dimension

The net force is the vector sum of forces acting on a particle or body. When an object is in equilibrium (either at rest or moving with constant velocity), the net force acting on it is zero. A vector can only have zero magnitudes if all of its components are zero or the forces acting against each other on the object are equal.

Explain that unbalanced forces cause motion or deformation

When two forces acting on an object are not equal in size, we say that they are unbalanced forces. This then causes some type of motion or deformation on an object.

Moments of forces

The moment of a force is a measure of the turning effect of the force about a point. The moment depends on the magnitude of the force and the length of the lever upon which the force acts.

Define torque

Torque, τ, is the tendency of a force to rotate an object about some axis. Torque is equal to force times the distance. The unit for torque is the Newton meter (Nm).

Define the law of moments

When an object is balanced (in equilibrium) the sum of the clockwise moments is equal to the sum of the anticlockwise moments. Force 1 x its distance from pivot = Force 2 x distance from the pivot.

Solve problems on the turning effect of a force

Analyze the center of gravity of different objects

Method of finding Center of Gravity of Different Objects

Look at the given plain and look at its weight. In this example, the plain will be a plank with a length of 16ft and a weight of 30lbs

Next, Identify the other weights on each side of the center point, in this example being 40lbs on the first side and 60lbs on the second side

Then, Identify a datum. A datum is either end of the plank that you will use as a starting point to measure the plank

Then, measure the length of the datum from the first weight, the center point, and the second point. The measurements were 1ft, 8ft, and 15ft

Then, create a table with the weight, their corresponding length from the datum, and multiply them to get the moment. (i.e. 40 x 1 = 40, 30 x 8 = 240)

Next, Add up each of the weights (being 130lbs total) and add up each of the moments (being 1180ft-lbs total)

Finally, divide the total moment by the total weight (1180 / 130) and the final value you get is the center of gravity from the datum (being 9.08ft)