Tuesday, September 7th, 2010

### Solution:

A scientific experiment has three types of variables: independent, dependent and controlled. Please click on this link to get details: http://www.sciencebuddies.org/mentoring/project_variables.shtml.

Saturday, July 24th, 2010

## Solution:

**First some definitions:**

A **neuron** is an electrically excitable cell that processes and transmits information by electrochemical signaling. On one end of the neuron are the dendrites (receiving end) and the other end is the transmitting end (axon terminal).

**Synapse:** One neuron connects to another neuron when the dendrite of one is connected to the axon terminal of the other. This connection is called a synapse.

**Dendrites** are the branched projections of a neuron that act to conduct the electrochemical stimulation received from other neural cells to the main part of the neuron from which the dendrites project. Dendrites form the main receiving part of neurons. Dendrites collect and funnel these signals to the soma and axon.

A **neurotransmitter** is a chemical that is released from a neuron.

**Synaptic Cleft**: The tiny space between two nerve cells across which the neurotransmitter diffuses

**Receptor**: Neurotransmitters cross the synapse where they may be accepted by the next neuron at a specialized site on a dendrite called a receptor.

Here are the detailed instructions for the “lost” neurotransmitter:

- You are currently on the receptor of a dendrite

- To get to the next neuron in the chain, you must travel the length of the neuron you are current on

- Travel across the dendrite

- Travel down the entire length of the axon

- Travel across the axon terminal

- At the synaptic cleft, bind with receptor sites on the neighboring neuron’s dendrite

Saturday, July 24th, 2010

### Solution:

A number a in the domain of a given function f is called a critical number ‘(a) = 0 or f ‘ is undefined at x = a.

Relative extrema are the minimums or maximum points on a part of a curve, while absolute extrema are the minimums and maximum points along the entire curve.

Now we are looking at the following curve:

f (x) =

To find the extrema, we take the first derivative and figure out at what value of x, the first derivate of the function equals to zero:

f’(x) = 2x-6

f’(3) = 0

As you can see the function is decreasing from negative infinity to 3, and increasing from 3 to infinity. The critical number is 3. There is only one relative (or local) minimum at (3, -9).

Friday, July 23rd, 2010

### Solution:

In the physical sciences, the amount of a sample is often given in terms of moles (i.e. Avogadro’s number, or 6.02214179 x 10^{23}):

Friday, July 23rd, 2010

### Solution:

First, let’s define what a Newton (N) is: “The Newton (N) is defined as the amount of force that, when acting on a 1 kg mass, produces an acceleration of 1 m/s/s (one meter per second per second). Therefore, 1 N = 1 kg =D7 1 m/s/s.”

The force of friction opposing the 325 N force is .25 * 925 N (which is equal to 231.25 N). The force pulling the crate is 325 N * cos(25), i.e. 294.55 N. (This is the component of force acting parallel to the floor.)

Take the difference between these two and you will have the net force pulling the crate (which is 63.3 N). Using Newton’s equation F = ma, you will find the acceleration by dividing the net force by the mass of the crate (the mass is 925 =/(one standard gravity [9.80665 m/s/s], or 94.32 kg). The acceleration is therefore 63.3 N / 94.32 kg, which equals 0.671 m/s/s.

Thursday, July 22nd, 2010

You roll a basketball and a bowling ball directly towards each other at the same speed. Predict what will happen to each after the two collide.

### Solution:

Let’s assume that this is an “elastic collision of unequal masses” (see http://en.wikipedia.org/wiki/Elastic_collision, which will help you visualize this). Let’s also assume that the weight of the basketball is 1 pound and the weight of the bowling ball is 2 pounds, and that the basket ball is traveling from east to west at a speed (v) of 9 miles per hour, and the bowling ball is traveling west to east at 9 miles per hour.

After the collision the bowling ball reverse direction and travel at 3 miles per hour, and the basketball will reverse direction and travel at 15 miles per hour.

Thursday, July 22nd, 2010

### Soluton:

We found the following picture of what’s inside a flower at

http://www.eduplace.com/science/hmxs/ls/pdf/2rs_1_3-3.pdf

Monday, July 19th, 2010

### Solution:

Scientific experiment has three types of variables: independent, dependent and controlled.

Please click on this link to get details:

http://www.sciencebuddies.org/mentoring/project_variables.shtml