IB Physics Unit 7

2/12/24 Gravitational Potential

1) Review Newton’s Law of Universal Gravitation and Gravitational Field

• Newtons law is the force of gravity one one mass by another

• The gravitational field is the force per unit mass experienced by a small point mass a distance r from a larger mass M

• Main difference is that field tells how one object interacts with anything else, force is how two objects interact with each other

• Gravitational Field can be represented by the equation, field lines, or a graph

2) Know when to use each Gravitational Potential Energy equation

• When gravity is not even (really large scales) MGH doesn’t work as well so we use [Ep = -G (m1m2/r)] which is close to the force equation but uses r instead of r squared

• Zero line is infinitely far away because if you were infinitely far away, there would be no gravity force. Any closer and it would fall into the energy well

• Therefore, negative work is required to bring an object closer

• New Quantity Gravitational Potential Energy: Work done to bring a small point mass from infinity to a distance r; potential energy per unit mass caused by central mass M

• The variable for Gravitational potential energy is V sub g

• GMM/R is used when there is a changing gravitational potential, and MGH is used when the gravitational potential is uniform.

3) Introduce the idea of gravitational potential and drawing equipotential lines

• Equipotential lines are lines of equal gravitational potential which make a circle around the earth (for example) whose strength are indicated by their density

• It would require no work for an object to orbit along one of those lines

• As lines get closer, they represent more energy

2/6/24 Power

1) Understand what is Power and how to calculate efficiency

• Lifting 100 1kg rocks 1m takes the same amount of work as moving a 100kg rock 1m and the same amount of work as moving a 1kg rock 100m. However, some of these tasks are obviously going to be harder. So why is that? Ultimately, it’s because they take different amounts of power

• New Quantity Power: The rate at which work is performed or the rate of energy transfer

• New Unit Watt: (derived unit Joules per second). Also, one horsepower is 745.7 W

• Power EQ: [P = W/T = FV] (← force times velocity)

• Efficiency is what percent of the power produced is actually going into changing the energy

• Efficiency EQ [useful work out/total work in = useful power out/total power in]

• You will never have an efficiency grater than 100 (which is 100% efficiency)

2) Understand the three equations, as well as the variables in each equation

• There are technically only two in the Equation Packet, but the third is useful and easy to get to

• The three equations are [W/T], [FV], [P = ∆E/t]

2/4/24 The Work-Energy Theorem

1) Understand the Work-Energy Theorem

• New Quantity Work: The change in mechanical energy of a system

• New Quantity Energy: The ability to do work. There are three types: Kinetic, gravitational potential, and spring potential

• Conservation of energy states that the total energy of an isolated system will always be constant. But what if there are outside forces or work?

• [Ei + W = Ef] is the work-energy theorem: Initial energy plus work is equal to the final energy of the system

• We got this from the fact the conservation of energy says Ei has to equal Ef. And since work is the change in energy, work is equal to Ef-Ei. This can be rearranged to result in the work-energy theorem equation

2) Solve problems involving work and energy

• Start by identifying the types of energy you started and ended with, and fill in the equation for the problem

• Ideally, solve algebraically with the variables first

• Positive work will result in more energy in the end

• Negative work results in a reduction of energy

1/31/24 Types of Energy EdPuzzles

1) Understand the variables and equations for each type of energy

For Gravitational Potential Energy [PEg = mgh]:

• Symbol is PEg (g is subscript) or Ug

• (m) is mass of the object

• (g) is the acceleration due to gravity

• (h) is the vertical height above the horizontal zero line

For Kinetic Energy (can never be negative) [KE = ½ mv²]:

• (m) is the mass of the object

• (v) is the velocity of the object

For Elastic Potential Energy (can never be negative) [PEe = ½ kx²]

• Symbol is PEe (e is subscript) or Ue

• (k) is the spring constant in Nm

• (x) is displacement from equilibrium, or rest, position

• slope of a force vs displacement graph is the spring constant of the spring

These are all scalar quantities

2) Understand the importance of the zero line for gravitational potential energy and equilibrium for elastic potential energy

• The zero line can be moved. You choose where to put it on every problem

• If the object’s center of mass is above the zero line, PEg will be positive.

• If the object’s center of mass is below the zero line, PEg will be negative.

• If the object’s center of mass is exactly on the zero line, PEg will be zero.

• Equilibrium is the point at which an object is not deformed. It is the resting position

1/30/24 The Work Equation

1) Identify and understand all variables in the Work equation

• The work equation is W = (F)(s)cos(θ)

• F represents the force applied

• S represents the amount of displacement

• (θ) is the angle between the force and direction of displacement

2) Describe what the sign of work is for various situations

• Work is positive when force and displacement are in the same direction

• Work is negative when force and displacement are in opposite directions

• Work is zero when force and displacement are perpendicular or when there is no displacement

• The closer the vectors are to each other, the more work you would do up until the angle is 90 and no work is done.

Further notes:

• Work is the product of force and displacement, but these are both vectors

• Multiplying vectors is more complicated than scalar quantities. There are two ways to do it. The first is called dot product, or scalar product, and to do this you take the component of the first vector that is in the direction of the second vector, and multiply it by the magnitude of the second vector: a x b = |a| x |b| cos(θ)

• The second is called cross product, or vector product, and this method finds a kind of area that goes with the vectors. The answer is a vector that is perpendicular to the other vectors

• Work is the dot product of force and displacement, so it is a scalar quantity.