Title: Solving harder physics problems
1Solving harder physics problems
2Objectives
- 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.
3Assessment
- 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. - Convert all given quantities to metric units if
needed. - How long does it take for the two cars to meet?
4Assessment
- 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?
5Physics terms
- variable
- conversion factor
- position
- velocity
- acceleration
6Equations
7Solving harder physics problems
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?
8Assumptions you can make
In most problems you may assume the following
- Assume there is no friction, unless you are told
otherwise. - 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.
9How do you start?
What are you asked for? What is given? What is
the relationship? What is the solution?
10Apply 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?
11Find 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?
12Find 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
time
13Find 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?
speed 2
speed 1
total distance
time
speed 1, speed 2, total distance
14What is the 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? What are you asked for? What is
given? What is the relationship?
time
speed 1, speed 2, total distance
15What is the solution?
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
speed 1, speed 2, total distance
16What is the solution?
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
speed 1, speed 2, total distance
The solution will require more than one equation!
17Multiple unknowns need multiple equations
- 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.
18Strategy for 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?
Brainstorm with a partner what three equations
could be used to solve this problem?
19Solving 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
20Solving 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
21Solving 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?
Relationships in this problem
General relationship
22Solving 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?
Relationships in this problem
General relationship
23Solving 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
24Solving 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
25Solving 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
26Solving 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
27Solving 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
28Solving 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
29Another approach
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?
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!
30Reference frame red 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?
asked given relationship solution
time
total distance 500 m, speed of blue bike ?
31Reference frame red 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?
asked given relationship solution
time
total distance 500 m, speed of blue bike 13
m/s
32The 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?
33The 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
34The 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?
time
distance, velocity
35The 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? What is the solution?
time
distance, velocity
36The 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? What is the solution?
time
distance, velocity
Whats wrong here?
37Covert to consistent units
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!
38Solve
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?
time
distance, velocity
39Assessment
- 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. - Convert all given quantities to metric units if
needed. - How long does it take for the two cars to meet?
40Assessment
- 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. - Convert all given quantities to metric units if
needed. - How long does it take for the two cars to meet?
41Assessment
- 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. - How long does it take for the two cars to meet?
42Assessment
- 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?
43Assessment
- 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?
wanted average speed for the entire trip
given dtotal 2.0 km, v1 15 m/s, v2 25
m/s relationships solution
44Assessment
- 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?
wanted average speed for the entire trip
given dtotal 2.0 km, v1 15 m/s, v2 25
m/s relationships solution
45Assessment
- 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?
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.