# Incline max angle physics problem

• JonathanSnow
In summary, the conversation discusses the design of an entrance ramp for a new megamart, with a maximum customer force of 20N and a 20kg grocery cart. The group explores the maximum angle at which the ramp should be built, with the conclusion that it should be approximately 5.8 degrees to maintain a force of 20N. Other methods of finding the angle are briefly considered, and it is determined that any larger angle will result in a greater force and potential customer complaints.
JonathanSnow
we have to design an entrance ramp for the new megamart. the maximum force customers will exert without complaint is 20N, ignoring friction at what maximum angle should the ramp be built assuming a full 20 kg grocery cart?

i've almost drawn at a blank it just seems like the question is missing something is there any other way besides trial and error, even miniscule hints would be appreciated

The variable is angle of the ramp. On this incline the tangential force on a 20kg stationary grocery cart should be 20N. The gravitational force is mg. How much is tangential at an angle theta? Can you solve for the angle?

im still confused a bit the angle is it 5.8ish I am not sure exactly what I am missing
f=mg sin(theta)

Last edited:
You didn't show much of your work there. Yes, it is 5.8ish if you mean degrees. It's hard to tell what you are missing if you don't say what you did or why you don't think it's right.

ok what i did was used the formula F=mg sin(Theta) and punched in
20=20(9.81) sin (theta)
20/196.2=sin(theta)
sin-1(.101...)=theta
theta = 5.85
?
so when i get this angle is that the maximum it can be?

At that angle holding a 20kg grocery cart at constant acceleration will need a force of 20N. If the angle is larger, the force is larger. And I guess that means the customers will complain. Well done.

thanks alot!

## 1. What is the maximum angle of incline in a physics problem?

The maximum angle of incline in a physics problem refers to the steepest angle at which an object can be placed on a surface without sliding down due to gravity. This angle is also known as the "critical angle" and is determined by the coefficient of friction between the object and the surface.

## 2. How is the maximum angle of incline calculated?

The maximum angle of incline can be calculated using the formula: θ = tan^-1(μ), where θ is the angle of incline and μ is the coefficient of friction between the object and the surface. This formula assumes that the object is on the verge of sliding down the incline.

## 3. What factors affect the maximum angle of incline?

The maximum angle of incline is affected by the coefficient of friction, the weight of the object, and the surface it is placed on. A higher coefficient of friction and a lighter object will result in a steeper maximum angle, while a smoother surface will decrease the maximum angle.

## 4. How does the maximum angle of incline relate to kinetic and potential energy?

The maximum angle of incline is related to the balance between kinetic and potential energy. At the maximum angle, the potential energy of the object is equal to the kinetic energy, meaning that the object has just enough energy to overcome the force of friction and slide down the incline.

## 5. Can the maximum angle of incline be exceeded?

Technically, yes, the maximum angle of incline can be exceeded if an external force is applied to the object to prevent it from sliding down. However, this would go against the laws of physics and is not a realistic scenario in most physics problems.

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