Algebraic Relations and Constantsname: ______

Algebraic Relations and ConstantsName: ______

In physics we are often interested in the effect that changing one variable has on another in a physical situation.

For example, the equation relating velocity, displacement and time is given by ______.

If we double the time it takes to move the same displacement the velocity will ______.

Problem 1: The electrical resistance of a material is given by the equation R = ρL/A where ρ is the resistivity of the material from which the resistor is made, L is the length of the resistor in meters, and A is the cross-sectional area of the resistor (m2).

What happens to the resistance if the length of the resistor is cut in half? Explain.

What happens to the resistance if the area of the resistor is cut in half? Explain.

What happens to the resistance if the material is changed to one with twice the resistivity and 1/3 of the length? Explain.

Problem 2: The period (time it takes for one complete cycle of motion) of a mass attached to a spring is given by the equation T = 2π where m is the mass attached to the spring (kg) and k is the spring constant which measures how stiff the spring is.

What happens to the period if the mass attached to the spring is increased by a factor of 4? Explain.

What happens to the period if the mass attached to the spring is decreased by a factor of 2? Explain.

What happens to the period if the mass attached is double and the spring is replaced with one that is 3 times more stiff? Explain.

Problem 3: A student makes the following claim: “Anytime you change a number in the numerator the total value of the equation increases and anytime you change a number in the denominator the total value of the equation decreases”. Do you agree or disagree with the student? Justify your answer.

Universal and physical constants are quite common in physics, describing quantities such as the permittivity of space or the gravitational constant. It is important that you not memorize their units, but be able to use knowledge of SI units to derive their units.

For example, the equation relating velocity, displacement and time is given by ______.

So the units for velocity would be ______.

How do we determine the units of the spring constant given the following equation for the force of a spring:

F = kx

Given that F is in Newtons and x is in meters?

How do we determine the units of the gravitational constant given the following equation for the force of gravity:

Given that F is in Newtons, M is mass in kilograms and r is distance in meters?

Practice Quiz

Problem 1: Consider the ideal gas law which states that PV=nRT where P is the pressure of the gas (Pa), V is the volume (m3), n is the number of moles of gas, T is the temperature of the gas (K) and R is the Rydberg constant.

Solve the equation for R.

What would happen to the volume of the gas if you doubled the pressure and tripled the temperature?

What are the units of the Rydberg constant?

Problem 2: How many grams are in 42.5 ng?

Problem 3: In an experiment you measure the radius of various spheres and determine their volume using water displacement. What should your graph to obtain data that is linear?