In physics, it is very important to clearly communicate your understanding of the concepts used when you answer questions on assignments, quizzes and exams.  

This method of problem-solving is known as GRASP.

Each step of the GRASP method of problem-solving is outlined in each tab.


  1. Read the question carefully
  2. State all the physical quantities using the correct symbol, units, significant digits and direction if required.


  1. Identify what you are required to determine, stating units and direction for vector quantities


  1. Draw a sketch or vector diagram.  Note the direction and if needed set up a coordinate system. For example, the left is negative and the right is positive.
  2. List possible relationships, assumptions or physical principles. A list of physics principles can be found on your Physics 30 Data Booklet
  3. Identify any constants you need and find them on your Physics Data Sheet
  4. Complete any unit conversions
  5. Write down an appropriate formula, whose variables are either given, required or can be found on the Physics Data Sheet.
  6. Rearrange the formula to solve for the unknown variable.
  7. Carefully substitute the known variables into the formula and simplify the math as well as the units.
  8. Check your work, units, significant digits and direction for vectors


Write your solution in a complete sentence, checking units, significant digits, rounding and direction.

These momentum examples are solved using the GRASP method of problem-solving.  If you have any questions about these examples be sure to contact the teacher right away.  Their contact info is the apple icon above. 

Determine the momentum of a vehicle with a mass of 2100 kg moving at a velocity of 22 m/s East.
Given:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»m«/mi»«mo»=«/mo»«mn»2100«/mn»«mo»§#160;«/mo»«mi»k«/mi»«mi»g«/mi»«mspace linebreak=¨newline¨»«/mspace»«mover»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«mo»=«/mo»«mn»22«/mn»«mstyle displaystyle=¨false¨»«mfrac bevelled=¨true¨»«mrow»«mo»§#160;«/mo»«mi»m«/mi»«/mrow»«mi»s«/mi»«/mfrac»«/mstyle»«mo»§#160;«/mo»«mo»[«/mo»«mi»E«/mi»«mo»]«/mo»«/math»
Required:
The momentum of the vehicle,  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨» «mover» «mi»p«/mi» «mo»§#8594;«/mo» «/mover» «/math»

Analysis and Solution:
Let east be the positive direction

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«mover»«mi»p«/mi»«mo»§#8594;«/mo»«/mover»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»m«/mi»«mover»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«/mtd»«/mtr»«mtr»«mtd»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mrow»«mo»(«/mo»«mn»2100«/mn»«mo»§#160;«/mo»«mi»k«/mi»«mi»g«/mi»«mo»)«/mo»«mo»(«/mo»«mo»+«/mo»«mn»22«/mn»«mstyle displaystyle=¨false¨»«mfrac bevelled=¨true¨»«mi»m«/mi»«mi»s«/mi»«/mfrac»«/mstyle»«mo»)«/mo»«/mrow»«/mtd»«/mtr»«mtr»«mtd»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»+«/mo»«mn»4«/mn»«mo».«/mo»«mn»6«/mn»«mo»§#215;«/mo»«msup»«mn»10«/mn»«mn»4«/mn»«/msup»«mo»§#160;«/mo»«mi»k«/mi»«mi»g«/mi»«mo»§#183;«/mo»«mstyle displaystyle=¨false¨»«mfrac bevelled=¨true¨»«mi»m«/mi»«mi»s«/mi»«/mfrac»«/mstyle»«/mtd»«/mtr»«/mtable»«/math»


Paraphrase:
The momentum of the vehicle is «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«/mtd»«mtd»«/mtd»«mtd»«mn»4«/mn»«/mtd»«/mtr»«/mtable»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«/mtd»«mtd»«/mtd»«mtd»«mo».«/mo»«/mtd»«/mtr»«/mtable»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«/mtd»«mtd»«/mtd»«mtd»«mn»6«/mn»«/mtd»«/mtr»«/mtable»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«/mtd»«mtd»«/mtd»«mtd»«mo»§#215;«/mo»«/mtd»«/mtr»«/mtable»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«/mtd»«mtd»«/mtd»«mtd»«mn»10«/mn»«/mtd»«/mtr»«/mtable»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«/mtd»«mtd»«/mtd»«mtd»«msup»«mrow»«/mrow»«mn»4«/mn»«/msup»«/mtd»«/mtr»«/mtable»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«/mtd»«mtd»«/mtd»«mtd»«mo»§#160;«/mo»«/mtd»«/mtr»«/mtable»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«/mtd»«mtd»«/mtd»«mtd»«mi»k«/mi»«/mtd»«/mtr»«/mtable»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«/mtd»«mtd»«/mtd»«mtd»«mi»g«/mi»«/mtd»«/mtr»«/mtable»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«/mtd»«mtd»«/mtd»«mtd»«mo»§#183;«/mo»«/mtd»«/mtr»«/mtable»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«/mtd»«mtd»«/mtd»«mtd»«mfrac bevelled=¨true¨»«mi»m«/mi»«mi»s«/mi»«/mfrac»«/mtd»«/mtr»«/mtable»«/math» [E]

In many countries, motorized scooters are a popular form of transportation.  If the total momentum of two people on a scooter is 7.20 × 10 3  kg · m/s [S] and their combined mass is 250 kg, determine the velocity of the people on the scooter.

Given
   «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«mover»«mi»p«/mi»«mo»§#8594;«/mo»«/mover»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»7«/mn»«mo».«/mo»«mn»20«/mn»«mo»§#215;«/mo»«msup»«mn»10«/mn»«mn»3«/mn»«/msup»«mo»§#160;«/mo»«mi»k«/mi»«mi»g«/mi»«mo»§#183;«/mo»«mfrac bevelled=¨true¨»«mi»m«/mi»«mi»s«/mi»«/mfrac»«mo»,«/mo»«mo»§#160;«/mo»«mfenced open=¨[¨ close=¨]¨»«mi»S«/mi»«/mfenced»«/mtd»«/mtr»«mtr»«mtd»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»-«/mo»«mn»7«/mn»«mo».«/mo»«mn»20«/mn»«mo»§#215;«/mo»«msup»«mn»10«/mn»«mn»3«/mn»«/msup»«mo»§#160;«/mo»«mi»k«/mi»«mi»g«/mi»«mo»§#183;«/mo»«mfrac bevelled=¨true¨»«mi»m«/mi»«mi»s«/mi»«/mfrac»«/mtd»«/mtr»«mtr»«mtd»«mi»m«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»250«/mn»«mo»§#160;«/mo»«mi»k«/mi»«mi»g«/mi»«/mtd»«/mtr»«/mtable»«/math»


Required

The velocity of the vehicle, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«/math»


Analysis and Solution

    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»p«/mi»«mo»§#8594;«/mo»«/mover»«mo»=«/mo»«mi»m«/mi»«mover»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«mspace linebreak=¨newline¨»«/mspace»«mover»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«mo»=«/mo»«mfrac»«mover»«mi»p«/mi»«mo»§#8594;«/mo»«/mover»«mi»m«/mi»«/mfrac»«mspace linebreak=¨newline¨»«/mspace»«mo»=«/mo»«mfrac»«mrow»«mo»-«/mo»«mn»7«/mn»«mo».«/mo»«mn»20«/mn»«mo»§#215;«/mo»«msup»«mn»10«/mn»«mn»3«/mn»«/msup»«mo»§#160;«/mo»«mi»k«/mi»«mi»g«/mi»«mo»§#183;«/mo»«mstyle displaystyle=¨true¨»«mfrac bevelled=¨true¨»«mi»m«/mi»«mi»s«/mi»«/mfrac»«/mstyle»«/mrow»«mrow»«mn»250«/mn»«mo»§#160;«/mo»«mi»k«/mi»«mi»g«/mi»«/mrow»«/mfrac»«mspace linebreak=¨newline¨»«/mspace»«mo»=«/mo»«mo»-«/mo»«mn»28«/mn»«mo».«/mo»«mn»8«/mn»«mo»§#160;«/mo»«mfrac bevelled=¨true¨»«mi»m«/mi»«mi»s«/mi»«/mfrac»«/math»

Paraphrase

 The velocity of the motorcycle and riders is 28.8 m/s [S].

An airplane has a momentum of 8.3 × 10 7  kg · m/s [N].  If the airplane is flying at a velocity of 990 km/h [N], determine its mass.

Given
   «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«mover»«mi»p«/mi»«mo»§#8594;«/mo»«/mover»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»8«/mn»«mo».«/mo»«mn»3«/mn»«mo»§#215;«/mo»«msup»«mn»10«/mn»«mn»7«/mn»«/msup»«mo»§#160;«/mo»«mi»k«/mi»«mi»g«/mi»«mo»§#183;«/mo»«mfrac bevelled=¨true¨»«mi»m«/mi»«mi»s«/mi»«/mfrac»«mo»,«/mo»«mo»§#160;«/mo»«mfenced open=¨[¨ close=¨]¨»«mi»N«/mi»«/mfenced»«/mtd»«/mtr»«mtr»«mtd»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»+«/mo»«mn»8«/mn»«mo».«/mo»«mn»3«/mn»«mo»§#215;«/mo»«msup»«mn»10«/mn»«mn»7«/mn»«/msup»«mo»§#160;«/mo»«mi»k«/mi»«mi»g«/mi»«mo»§#183;«/mo»«mfrac bevelled=¨true¨»«mi»m«/mi»«mi»s«/mi»«/mfrac»«/mtd»«/mtr»«mtr»«mtd»«mover»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»990«/mn»«mo»§#160;«/mo»«mfrac bevelled=¨true¨»«mrow»«mi»k«/mi»«mi»m«/mi»«/mrow»«mi»h«/mi»«/mfrac»«mo»,«/mo»«mo»§#160;«/mo»«mfenced open=¨[¨ close=¨]¨»«mi»N«/mi»«/mfenced»«/mtd»«/mtr»«mtr»«mtd»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»+«/mo»«mn»990«/mn»«mfrac»«menclose notation=¨downdiagonalstrike¨»«mi»k«/mi»«mi»m«/mi»«/menclose»«menclose notation=¨downdiagonalstrike¨»«mi»h«/mi»«/menclose»«/mfrac»«mo»§#183;«/mo»«mfrac»«mrow»«mn»1000«/mn»«mi»m«/mi»«mo»§#183;«/mo»«/mrow»«mrow»«mn»1«/mn»«menclose notation=¨downdiagonalstrike¨»«mi»k«/mi»«mi»m«/mi»«/menclose»«/mrow»«/mfrac»«mfrac»«mrow»«mn»1«/mn»«mo»§#160;«/mo»«menclose notation=¨downdiagonalstrike¨»«mi»h«/mi»«/menclose»«/mrow»«mrow»«mn»3600«/mn»«mo»§#160;«/mo»«mi»s«/mi»«/mrow»«/mfrac»«/mtd»«/mtr»«mtr»«mtd»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»+«/mo»«mn»275«/mn»«mo»§#160;«/mo»«mfrac bevelled=¨true¨»«mi»m«/mi»«mi»s«/mi»«/mfrac»«/mtd»«/mtr»«/mtable»«/math»


Required

The velocity of the vehicle, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«/math»


Analysis and Solution

    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»p«/mi»«mo»=«/mo»«mi»m«/mi»«mi»v«/mi»«mspace linebreak=¨newline¨»«/mspace»«mi»m«/mi»«mo»=«/mo»«mfrac»«mi»p«/mi»«mi»v«/mi»«/mfrac»«mspace linebreak=¨newline¨»«/mspace»«mo»=«/mo»«mfrac»«mrow»«mo»+«/mo»«mn»8«/mn»«mo».«/mo»«mn»3«/mn»«mo»§#215;«/mo»«msup»«mn»10«/mn»«mn»7«/mn»«/msup»«mo»§#160;«/mo»«mi»k«/mi»«mi»g«/mi»«mo»§#183;«/mo»«mstyle displaystyle=¨true¨»«mfrac bevelled=¨true¨»«mi»m«/mi»«mi»s«/mi»«/mfrac»«/mstyle»«/mrow»«mrow»«mn»275«/mn»«mo»§#160;«/mo»«mstyle displaystyle=¨true¨»«mfrac bevelled=¨true¨»«mi»m«/mi»«mi»s«/mi»«/mfrac»«/mstyle»«/mrow»«/mfrac»«mspace linebreak=¨newline¨»«/mspace»«mo»=«/mo»«mn»3«/mn»«mo».«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mo»§#215;«/mo»«msup»«mn»10«/mn»«mn»5«/mn»«/msup»«mo»§#160;«/mo»«mi»k«/mi»«mi»g«/mi»«/math»

Paraphrase

 The mass of the airplane is 3.0 × 10 5  kg.