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Physics Formulas TI 84

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Physics Formulas TI 84 - Formula Quest

Physics Formulas on the TI-84 Calculator

The TI-84 calculator is a powerful tool that can assist students and professionals in solving complex physics problems. Its functionality includes built-in physics formulas, programmable features, and the ability to store custom formulas for quick reference.

Using Built-In Functions

The TI-84 calculator includes several built-in functions that can be useful for physics calculations. These functions include trigonometric operations, logarithmic functions, and statistical analyses. Here are some common physics formulas and how to use them on the TI-84.

Trigonometric Functions

In physics, trigonometric functions are often used to solve problems involving angles and distances. The TI-84 can easily handle sine, cosine, and tangent calculations.

Example: Calculating the Height of an Object

Suppose you need to find the height h of a building. You are standing 50 meters away from the building and measure the angle of elevation to the top of the building to be 30 degrees.

  1. Use the tangent function: tan(θ) = opposite/adjacent
  2. Here, θ = 30°, and the adjacent side is 50 meters.
  3. Enter the following into the TI-84: tan(30)
  4. Multiply the result by 50 to find the height: 50 * tan(30)

The height of the building is approximately 28.87 meters.

Logarithmic Functions

Logarithmic functions are used in physics for problems involving exponential growth or decay, such as radioactive decay or population growth.

Example: Radioactive Decay

The formula for radioactive decay is N(t) = N0 e−λt, where:

  • N(t) is the quantity that still remains after time t,
  • N0 is the initial quantity,
  • λ is the decay constant,
  • t is the time.

Suppose you have a sample with an initial quantity of 100 grams and a decay constant of 0.1. You want to find out how much of the sample remains after 5 years.

  1. Enter the following into the TI-84: 100 * e−0.1 * 5

The remaining quantity is approximately 60.65 grams.

Storing and Using Custom Formulas

The TI-84 allows users to store custom formulas for quick access. This is particularly useful for repetitive calculations.

Storing a Formula

Example: Kinetic Energy Formula

The formula for kinetic energy is KE = 0.5mv2, where:

  • KE is the kinetic energy,
  • m is the mass,
  • v is the velocity.
  1. Press PRGM and select New to create a new program.
  2. Name your program (e.g., KINETIC).
  3. Enter the following code to prompt for mass and velocity:
:Prompt M
:Prompt V
:Disp 0.5*M*V2
  1. Press 2nd and QUIT to save.

Using the Stored Formula

  1. Press PRGM, select the program KINETIC, and press ENTER.
  2. Follow the prompts to enter the mass and velocity.
  3. The TI-84 will display the kinetic energy.

Example Usage:

For a mass of 10 kg and a velocity of 5 m/s:

  1. Enter 10 when prompted for mass.
  2. Enter 5 when prompted for velocity.

The calculator will display 125 Joules.

Advanced Features

The TI-84 can also be used for more advanced physics calculations, such as those involving differential equations or vector operations. For these tasks, using the built-in programming capabilities or downloading specialized apps and programs can be very helpful.

Solving Differential Equations

Example: Simple Harmonic Motion

The differential equation for simple harmonic motion is d2x/dt2 + ω2x = 0.

  1. Use the TI-84's differential equation solver by pressing MATH, selecting 9:Solver, and entering the equation in the form of 0 =.
  2. Input initial conditions and solve.

Vector Operations

Example: Adding Vectors

To add vectors, use the vector operations available in the TI-84.

  1. Enter the vectors as lists: L1 for the first vector and L2 for the second vector.
  2. Use the sum( function to add corresponding components: sum(L1+L2).

This feature simplifies complex vector operations that are common in physics problems.

Conclusion

The TI-84 calculator is a versatile tool for solving physics problems. It can handle trigonometric, logarithmic, and exponential functions, store and use custom formulas, and perform advanced calculations like solving differential equations and vector operations. By leveraging the capabilities of the TI-84, students and professionals can efficiently solve a wide range of physics problems.

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