How to Calculate Maximum Angle for Ramps in Supermarkets | Basic Physics Help

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SUMMARY

The discussion focuses on calculating the maximum angle for ramps in supermarkets to ensure that customers can push grocery carts without exceeding a force of 20N. The relevant equations include F=mg and mg*sin(theta)=Fapp, where Fapp is the applied force. The correct maximum angle, as derived from the calculations, is 5.9 degrees, although some participants initially arrived at 3.9 degrees due to miscalculations. The importance of ensuring calculators are set to the correct mode is emphasized to avoid errors in trigonometric calculations.

PREREQUISITES
  • Understanding of basic physics concepts such as force, mass, and acceleration.
  • Familiarity with trigonometric functions, specifically sine and angles.
  • Ability to perform calculations involving gravitational force (F=mg).
  • Knowledge of how to set calculator modes for trigonometric calculations (degrees vs. radians).
NEXT STEPS
  • Review the principles of static friction and its impact on ramp design.
  • Learn about the application of Newton's laws in real-world scenarios.
  • Explore advanced trigonometric functions and their applications in engineering.
  • Investigate design standards for accessibility in public spaces, particularly for ramps.
USEFUL FOR

This discussion is beneficial for engineering students, physics learners, and designers involved in creating accessible environments, particularly in retail settings.

AfroQueen
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Homework Statement


in the design of a spermarket there are to be several ramps connecting different parts of the store. customers will have to push grocery cats up the ramps and it is obviously desirable that this is not be too difficult. The engineer has done a survey and found that almost no noe complains if the force directed up the ramp is no more than 20N. Ignoring friction at what maximum angle (theta) should the ramps be built assuming a full 30kg grocery cart.


Homework Equations


F=mg
mg sin(theta)= Fapp
Fapp= force applied=20N

The Attempt at a Solution


ok i understand this question or so i thought but every time i try to work it out i don't get the answer which is supposed to be 5.9 degrees... Here's my work
F=mg
F=30*9.8
F=294N

mg *sin(theta)=20N
294*sin(theta)=20N
sin(theta)=.068027
theta=3.9 ?
 
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How did you create your second equation?
 
The answer must be a mistake..
You're work appears fine to me.
 
hyemal.zephyr said:
How did you create your second equation?

the secondd equation comes because friction is ignored in this problem so in the equation mg*sin(theta)-(static kinetic energy)*cos(theta) the static kinetic energy doesn't apply so you can think of it as 0... so you're left with mg*sin(theta) and since you need to make sure that the customers don't exceed a certain force (because they will complain) i set that equation equal to that certain force and that would give you the maximum angle...
 
Maybe_Memorie said:
The answer must be a mistake..
You're work appears fine to me.

thats what i keep saying to myself but my friend said she was able to get the same answer as the one provided in the book...
 
is your calculator in the correct mode?
 
Chip90 said:
is your calculator in the correct mode?

yeahi tried it in degree mode and i tried just putting it into radian mode and then just converting but i still get the same wrong answer...
 
Chip90 said:
is your calculator in the correct mode?

also do you think its has anything to do with my work?
or equations?
 

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