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

In summary, the engineer has found that a force of 20N is needed to push a grocery cart up a ramp with a slope of 3.9 degrees. If friction is ignored, the second equation produces the maximum angle for the ramps.
  • #1
AfroQueen
7
0

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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  • #2
How did you create your second equation?
 
  • #3
The answer must be a mistake..
You're work appears fine to me.
 
  • #4
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...
 
  • #5
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...
 
  • #6
is your calculator in the correct mode?
 
  • #7
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...
 
  • #8
Chip90 said:
is your calculator in the correct mode?

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

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

What is the difference between speed and velocity?

Speed is a measure of how fast an object is moving, while velocity is a measure of how fast an object is moving in a specific direction. Therefore, velocity includes both the speed and direction of an object's motion.

What is the difference between mass and weight?

Mass is a measure of the amount of matter in an object, while weight is a measure of the force of gravity acting on an object. Mass is constant, while weight can change depending on the strength of gravity on an object.

How do I calculate acceleration?

Acceleration is calculated by dividing the change in velocity by the change in time. The equation for acceleration is a = (vf - vi)/t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

What is Newton's First Law of Motion?

Newton's First Law of Motion states that an object at rest will stay at rest and an object in motion will stay in motion with a constant velocity unless acted upon by an unbalanced force. In other words, objects will continue to do what they are doing unless a force is applied to change their motion.

What is the difference between potential and kinetic energy?

Potential energy is the energy that an object has due to its position or condition, such as gravitational potential energy or elastic potential energy. Kinetic energy is the energy an object has due to its motion. In other words, potential energy is stored energy, while kinetic energy is the energy of motion.

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