Solving harder physics problemsSolving harder physics problems

• Convert quantities from one unit to another using appropriate conversion factors.

• Use algebraic models to analyze and solve multi-step problems mathematically.

• Use multiple independent equations to solve for multiple variables.

ObjectivesObjectives

1. Two cars are initially separated by 1.0 km and traveling towards each other. One car travels at 20 miles per hour and the second car travels at 20 meters per second.

a) Convert all given quantities to metric units if needed.

a) How long does it take for the two cars to meet?

AssessmentAssessment

2. A car travels a total distance of 2.0 kilometers. It travels the first half of the distance at a constant speed of 15 m/s. It travels the second half of the distance at a constant speed of 25 m/s. What is the average speed of the car?

AssessmentAssessment

• variable

• conversion factor

• position

• velocity

• acceleration

Physics termsPhysics terms

EquationsEquations

Two bicyclists approach each other on the same road. One has a speed of 5.0 m/s and the other has a speed of 8.0 m/s. They are 500 meters apart. How long will it be before they meet?

Solving harder physics problemsSolving harder physics problems

1. Assume there is no friction, unless you are told otherwise.

2. Velocities are constant unless you know otherwise.

3. Initial position, initial time, and initial velocity are zero unless you know otherwise. zero, unless you know otherwise.

In most problems you may assume the following:

Assumptions you can makeAssumptions you can make

What are you asked for?

What is given?

What is the relationship?

What is the solution?

How do you start?How do you start?

Two bicyclists approach each other on the same road. One has a speed of 5.0 m/s and the other has a speed of 8.0 m/s. They are 500 meters apart. How long will it be before they meet?

Apply the four step methodApply the four step method

Two bicyclists approach each other on the same road. One has a speed of 5.0 m/s and the other has a speed of 8.0 m/s. They are 500 meters apart. How long will it be before they meet?

What are you asked for?

Find wanted and given valuesFind wanted and given values

Two bicyclists approach each other on the same road. One has a speed of 5.0 m/s and the other has a speed of 8.0 m/s. They are 500 meters apart. How long will it be before they meet?

What are you asked for?

What is given?

time

Find wanted and given valuesFind wanted and given values

time

Two bicyclists approach each other on the same road. One has a speed of 5.0 m/s and the other has a speed of 8.0 m/s. They are 500 meters apart. How long will it be before they meet?

What are you asked for?

What is given?

speed 2speed 1 total distance

speed 1, speed 2, total distance

Find wanted and given valuesFind wanted and given values

time

Two bicyclists approach each other on the same road. One has a speed of 5.0 m/s and the other has a speed of 8.0 m/s. They are 500 meters apart. How long will it be before they meet?

What are you asked for?

What is given?

What is the relationship?

time

What is the relationship?What is the relationship?

speed 1, speed 2, total distance

Two bicyclists approach each other on the same road. One has a speed of 5.0 m/s and the other has a speed of 8.0 m/s. They are 500 meters apart. How long will it be before they meet?

What are you asked for?

What is given?

What is the relationship?

What is the solution?

time

What is the solution?What is the solution?

speed 1, speed 2, total distance

Two bicyclists approach each other on the same road. One has a speed of 5.0 m/s and the other has a speed of 8.0 m/s. They are 500 meters apart. How long will it be before they meet?

What are you asked for?

What is given?

What is the relationship?

What is the solution?

time

What is the solution?What is the solution?

speed 1, speed 2, total distance

The solution will require more than one equation!

In this problems, there are three unknowns:

•Although we know the TOTAL distance, each bicyclist will travel a different portion of that distance. (d1, d2)

•The wanted variable is time ( t )

To solve for three unknown quantities, three independent equations are needed.

Multiple unknowns need multiple equationsMultiple unknowns need multiple equations

Two bicyclists approach each other on the same road. One has a speed of 5.0 m/s and the other has a speed of 8.0 m/s. They are 500 meters apart. How long will it be before they meet?

Strategy for solving the problem Strategy for solving the problem

Brainstorm with a partner: what three equations could be used to solve this problem?

Solving the problem Solving the problem

General relationship:

Two bicyclists approach each other on the same road. One has a speed of 5.0 m/s and the other has a speed of 8.0 m/s. They are 500 meters apart. How long will it be before they meet?

Solving the problem Solving the problem

Two bicyclists approach each other on the same road. One has a speed of 5.0 m/s and the other has a speed of 8.0 m/s. They are 500 meters apart. How long will it be before they meet?

General relationship:

Solving the problem Solving the problem

Relationships in this problem:

Two bicyclists approach each other on the same road. One has a speed of 5.0 m/s and the other has a speed of 8.0 m/s. They are 500 meters apart. How long will it be before they meet?

General relationship:

Relationships in this problem:

Solving the problem Solving the problem

Two bicyclists approach each other on the same road. One has a speed of 5.0 m/s and the other has a speed of 8.0 m/s. They are 500 meters apart. How long will it be before they meet?

General relationship:

Solving the problem Solving the problem Two bicyclists approach each other on the same road. One has a speed of 5.0 m/s and the other has a speed of 8.0 m/s. They are 500 meters apart. How long will it be before they meet?

Solve for d1 and d2:

Solve for d1 and d2:

Solving the problem Solving the problem Two bicyclists approach each other on the same road. One has a speed of 5.0 m/s and the other has a speed of 8.0 m/s. They are 500 meters apart. How long will it be before they meet?

Substitute:

Solving the problem Solving the problem Two bicyclists approach each other on the same road. One has a speed of 5.0 m/s and the other has a speed of 8.0 m/s. They are 500 meters apart. How long will it be before they meet?

Solve for d1 and d2:

Substitute:

Solving the problem Solving the problem Two bicyclists approach each other on the same road. One has a speed of 5.0 m/s and the other has a speed of 8.0 m/s. They are 500 meters apart. How long will it be before they meet?

Solve for d1 and d2:

Substitute:

Solve for wanted variable:

Solving the problem Solving the problem Two bicyclists approach each other on the same road. One has a speed of 5.0 m/s and the other has a speed of 8.0 m/s. They are 500 meters apart. How long will it be before they meet?

Solve for d1 and d2:

Substitute:

Solve for wanted variable:

Solving the problem Solving the problem Two bicyclists approach each other on the same road. One has a speed of 5.0 m/s and the other has a speed of 8.0 m/s. They are 500 meters apart. How long will it be before they meet?

Solve for d1 and d2:

Another approach Another approach

Learning to solve tough problems using multiple equations is a very useful skill.

For this particular problem there is an easier way: let the red bike be your reference frame!

Two bicyclists approach each other on the same road. One has a speed of 5.0 m/s and the other has a speed of 8.0 m/s. They are 500 meters apart. How long will it be before they meet?

Two bicyclists approach each other on the same road. One has a speed of 5.0 m/s and the other has a speed of 8.0 m/s. They are 500 meters apart. How long will it be before they meet?

Reference frame: red bikeReference frame: red bike

asked:

given:

relationship:

solution:

time

total distance = 500 m, speed of blue bike = ?

Two bicyclists approach each other on the same road. One has a speed of 5.0 m/s and the other has a speed of 8.0 m/s. They are 500 meters apart. How long will it be before they meet?

Reference frame: red bikeReference frame: red bike

asked:

given:

relationship:

solution:

time

total distance = 500 m, speed of blue bike = 13 m/s

In solving problems, if units are NOT consistent you must convert. For example:

How long does it take a car traveling at 30 mph to travel across an intersection that is 18 m wide?

What is asked for?

The importance of unitsThe importance of units

In solving problems, if units are NOT consistent you must convert. For example:

How long does it take a car traveling at 30 mph to travel across an intersection that is 18 m wide?

What is asked for?

What is given?

time

The importance of unitsThe importance of units

In solving problems, if units are NOT consistent you must convert. For example:

How long does it take a car traveling at 30 mph to travel across an intersection that is 18 m wide?

What is asked for?

What is given?

What is the relationship?

distance, velocity

The importance of unitsThe importance of units

time

In solving problems, if units are NOT consistent you must convert. For example:

How long does it take a car traveling at 30 mph to travel across an intersection that is 18 m wide?

What is asked for?

What is given?

What is the relationship?

What is the solution?

The importance of unitsThe importance of units

time

distance, velocity

In solving problems, if units are NOT consistent you must convert. For example:

How long does it take a car traveling at 30 mph to travel across an intersection that is 18 m wide?

What is asked for?

What is given?

What is the relationship?

What is the solution?

What’s wrong here?

The importance of unitsThe importance of units

time

distance, velocity

How long does it take a car traveling at 30 mph to travel across an intersection that is 18 m wide?

Convert this velocity to metric units!

Covert to consistent unitsCovert to consistent units

In solving problems, if units are NOT consistent you must convert. For example:

How long does it take a car traveling at 30 mph to travel across an intersection that is 18 m wide?

What is asked for?

What is given?

What is the relationship?

What is the solution?

SolveSolve

time

distance, velocity

1. Two cars are initially separated by 1.0 km and traveling towards each other. One car travels at 20 miles per hour and the second car travels at 20 m/s.

a) Convert all given quantities to metric units if needed.

a) How long does it take for the two cars to meet?

AssessmentAssessment

1. Two cars are initially separated by 1.0 km and traveling towards each other. One car travels at 20 miles per hour and the second car travels at 20 m/s.

a) Convert all given quantities to metric units if needed.

a) How long does it take for the two cars to meet?

AssessmentAssessment

1. Two cars are initially separated by 1.0 km and traveling towards each other. One car travels at 20 miles per hour and the second car travels at 20 m/s.

b) How long does it take for the two cars to meet?

AssessmentAssessment

2. A car travels a total distance of 2.0 kilometers. It travels the first half of the distance at a constant speed of 15 m/s. It travels the second half of the distance at a constant speed of 25 m/s. What is the average speed of the car?

AssessmentAssessment

wanted: average speed for the entire trip

given: dtotal = 2.0 km, v1 = 15 m/s, v2 = 25 m/s

relationships:

solution:

2. A car travels a total distance of 2.0 kilometers. It travels the first half of the distance at a constant speed of 15 m/s. It travels the second half of the distance at a constant speed of 25 m/s. What is the average speed of the car?

AssessmentAssessment

2. A car travels a total distance of 2.0 kilometers. It travels the first half of the distance at a constant speed of 15 m/s. It travels the second half of the distance at a constant speed of 25 m/s. What is the average speed of the car?

AssessmentAssessment

wanted: average speed for the entire trip

given: dtotal = 2.0 km, v1 = 15 m/s, v2 = 25 m/s

relationships:

solution:

2. A car travels a total distance of 2.0 kilometers. It travels the first half of the distance at a constant speed of 15 m/s. It travels the second half of the distance at a constant speed of 25 m/s. What is the average speed of the car?

AssessmentAssessment

Notice that the average velocity was NOT 20 m/s!

The car spend more time going slower, so the average velocity was less than 20 m/s.