Solving harder physics problems

1
Solving harder physics problems
2
Objectives

• 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.

3
Assessment

• 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?

4
Assessment

1. 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?

5
Physics terms

• variable
• conversion factor
• position
• velocity
• acceleration

6
Equations
7
Solving 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?
8
Assumptions 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.

9
How do you start?
What are you asked for? What is given? What is
the relationship? What is the solution?
10
Apply 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?
11
Find 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?
12
Find 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
13
Find 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
14
What 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
15
What 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
16
What 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!
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Multiple 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.

18
Strategy 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?
19
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
20
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
21
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?
Relationships in this problem
General relationship
22
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?
Relationships in this problem
General relationship
23
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
24
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
25
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
26
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
27
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
28
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
29
Another 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!
30
Reference 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 ?
31
Reference 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
32
The 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?
33
The 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
34
The 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
35
The 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
36
The 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?
37
Covert 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!
38
Solve
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
39
Assessment

• 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?

40
Assessment

• 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?

41
Assessment

• 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?

42
Assessment

1. 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?

43
Assessment

1. 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
44
Assessment

1. 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
45
Assessment

1. 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.