Earth Science Lab: Angle of Repose

One of my goals in the last couple of years is to incorporate more math into my Earth Science course.  This lab allows students to explore the angle of repose, or the angle at which a consolidated slope can get before it becomes dangerously close to some sort of mass movement/wasting event.  Students are going to explore the angle at which a particular sediment, mostly sand, will begin to slide down slope.  Here is a copy of the angle of repose lab sheet that students used to help them explore this concept.

angle of repose lab

The materials that you are going to need as a teacher are:

  • cups, I used graduated beakers so that students could document exacly how much sand they ended up using.
  • sand, I just "borrowed" a sand bag that our school was using to keep the halls from flooding.  Don't worry, I did it after the monsoon season for our area.
  • large trays, I used lab trays, but last year I just used pizza boxes and those worked well if you don't have the lab trays.  Just know that it was a little messier with the pizza boxes.  Students can also just use tables or desks, but having a tray will contain the sand better so you don't get it all over your floor.
  • rulers, preferably 2 rulers for each group.

Teacher Procedure:

  • The first thing I did was actually explain what the angle of repose is.
  • Next I taught them a little trigonometry.  They used the inverse tangent formula to find the angle.  Angle of repose=Tan-1(h/r)
  • I then passed out the Angle of Repose lab sheet which really helps them perform the lab correctly.

Things we discovered as a class to make this lab better.

  • To measure the radius of the sand pile, students found it easier to lay one of the ruler on the tray first, and then pour the sand on the center of the ruler, at about 15 cm.  They could then take the difference between one side of the sand pile and the other to find the diameter.  Finally they could then divide the diameter by 2 in order to get the radius.
    • Angle of repose lab
  • Take some time as a teacher to teach students how to use their calculator to get the inverse tangent.  It is amazing how many high school students still do not know how to use the 2nd function key.
  • If you don't have scientific calculators and some of my students didn't, then they can just go to and long click the tangent button until it says "atan" which is the same as the inverse tangent.
  • Before students begin the Angle of Repose lab, make sure that you let them know to be careful not to bump their desk or a neighbors table as that will cause artificial landslides.
  • Students discovered that one of the easier methods of measuring the height of their sand pile was to take the second ruler and stand it up vertically while gently placing or holding a pencil slightly above the pile trying their best not to cause an artificial landslide.
  • Let students know also well in advance that they shouldn't put their materials away prematurely as some of the lab follow up questions require them to have a sand pile.
  • Due to the lack of aweome scientific equipment, some of their angles were off.  Have them take all 4 trials and get an average as that should help show the what their angle of repose is most likely to be.
  • In science you of course are going to use the metric system side of the ruler.  I didn't let my students know this year, but will next year that they should be using milimeters instead of centimeters.  I think their angles of repose will be more accurate if they are not rounding off centimeters to halves and quarters and instead using the milimeter mark.

Time: 55 Minutes

  • I only had 2 class where students weren't quite able to finish the lab before the bell rang.  I went ahead and gave them 10 minutes the next day.

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