I have 2 questions...one can someone please read my question posted around noon today called Lab for physics? Thanks..and secondly, I have to derive some equation. I am supposed to show a=gtantheta and find this from m (mass) L (length). The question also mentions the verical axis..nothing really helpful! Any ideas on how to do this derivation?
see below, but be certain to read this.
http://www.batesville.k12.in.us/physics/PhyNet/Mechanics/Circular%20Motion/labs/cf_and_speed.htm
Consider the bob spinning: centripetal force is outward, and gravity is downward.
Then the string makes the angle theta with
tan theta= mg/m*a =g/a where a is centripetal acceleration (v^2/r)
If you measure the other angle, then tan theta is a/g, so it depends on which angle you are measuring. Normally, we measure the first, string angle from horizontal.
So I understand the lab thing now completely! Thanks so much..and I sort of understand what you are doing for this derivation, but can you give some more of an explanation for where you are getting the equations from? Thanks a million!
centripetalforce= m*v^2/r where m is the mass of the spinning mass
gravity force holding it= mg where m is the washer weights
If r is constant, the two forces are equal, set them equal.
sometimes centripetal force is written as mw^2 r where w is angular velocity, but it is easily shown as above.
You measured period to go around, so
v=2PI r/Period
The rest is math, and critiquing error.
Certainly! Let's start with your first question. To find your previous question posted around noon today called "Lab for physics," you can follow these steps:
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Now, let's move on to your second question about deriving the equation a = g * tan(theta) using mass (m) and length (L), with a reference to the vertical axis.
To derive the equation a = g * tan(theta) from the given information, you can consider the following steps:
1. Start by defining the variables:
a - Acceleration
g - Acceleration due to gravity
theta - Angle made by the vertical axis
2. Consider a pendulum of length L, with a mass m attached to its end. The pendulum is initially at rest and then released from an angle theta away from the vertical axis. As the pendulum swings, the mass experiences an acceleration given by a.
3. Resolve the gravitational force acting on the mass into two components: one along the direction of motion (tangential) and the other perpendicular to it (radial).
4. The radial component of the gravitational force does not contribute to the tangential acceleration of the mass. Thus, we only focus on the tangential component.
5. The tangential component of the gravitational force can be expressed as mg * sin(theta), where mg is the total gravitational force acting on the mass, and sin(theta) represents the ratio of the length of the opposite side (mg * sin(theta)) to the hypotenuse (mg).
6. By Newton's second law, we know that Force = Mass * Acceleration. Therefore, the tangential component of the gravitational force (mg * sin(theta)) is equal to m * a.
7. Equating the tangential component of the gravitational force to m * a, we get:
mg * sin(theta) = m * a
8. Divide both sides of the equation by m:
g * sin(theta) = a
9. Since tan(theta) = sin(theta) / cos(theta), we can substitute sin(theta) with tan(theta) / cos(theta):
g * (tan(theta) / cos(theta)) = a
10. Simplify the equation by multiplying both sides by cos(theta):
g * tan(theta) = a * cos(theta)
11. Since cos(theta) represents the ratio of the adjacent side (a * cos(theta)) to the hypotenuse (a), we can simplify the equation further:
g * tan(theta) = a * cos(theta) becomes
g * tan(theta) = a
Therefore, we have derived the equation a = g * tan(theta) using the given information of mass (m), length (L), and a reference to the vertical axis.