How to calculate the gravity on a hill?

In summary: So if you're calculating the force down the slope and you see a value of 5 N, you know you've accidentally calculated the force up the slopeIn summary, the conversation discusses calculating the component of weight acting down an inclined plane with a 25 degree angle using the formula Fgravity,x = Fgravity sin(a). The correct triangle to use is one with the weight vector acting straight down as the hypotenuse. In an exam, if unsure whether to use sin or cos, consider that the force calculated should approach zero when the angle of the slope is reduced towards zero degrees.
  • #1
caspeerrr
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0
Member advised to use the homework template for posts in the homework sections of PF.
The question is about a box with no movement standing on a hill. The hill has an angle of 25 degrees. The box has a mass of 40 kg.
1. Calculte the gravity
This I still get: F= M x A = 40 x 9,81 = 3,9 x 10^2
The next question tough:
2. Calculate the component Fgravity,x off the gravity alongside the hill.
The component I think they ment is marked on the picture included.

What I did was 390 / sin(25) because the opposite is known (the gravity) and you want to calculate the hypotenuse. The answer indicates this as the right answer tough: Fgravity,x = Fgravity sin(a) = 165,8

Why do they multiply when you should divide?
Am I missing something?
Thanks in advance!
Knipsel.PNG
 
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  • #2
caspeerrr said:
What I did was 390 / sin(25) because the opposite is known (the gravity) and you want to calculate the hypotenuse.
You want the component of the weight acting down the incline. When finding the component of a vector using a right triangle, the full vector is always the hypotenuse. (The components are always smaller than the full vector.)

You're using the wrong triangle: Draw the weight vector acting straight down. That's the hypotenuse of the correct triangle.
 
  • #3
Check this out: Inclined Planes
 
  • #4
Doc Al said:
You want the component of the weight acting down the incline. When finding the component of a vector using a right triangle, the full vector is always the hypotenuse. (The components are always smaller than the full vector.)

You're using the wrong triangle: Draw the weight vector acting straight down. That's the hypotenuse of the correct triangle.
Doc Al said:
You want the component of the weight acting down the incline. When finding the component of a vector using a right triangle, the full vector is always the hypotenuse. (The components are always smaller than the full vector.)

You're using the wrong triangle: Draw the weight vector acting straight down. That's the hypotenuse of the correct triangle.

Aaah I get it, thank you!
 
  • #5
If you find yourself in an exam and can't remember if it's sin or cos... consider what happens if the angle of the slope is reduced towards zero degrees (no slope). The force you calculate down the slope should approach zero. Your calculator will tell you sin(0)=0 but cos(0)=1.
 

Related to How to calculate the gravity on a hill?

1. How do I determine the slope of the hill?

The slope of a hill can be calculated by dividing the vertical change in elevation by the horizontal distance. This can be measured using a topographic map or by physically measuring the hill.

2. What is the formula for calculating the gravitational force on a hill?

The formula for calculating the gravitational force on a hill is F = mg, where F is the gravitational force, m is the mass of the object, and g is the acceleration due to gravity. The value of g can vary slightly depending on the elevation and location on the hill.

3. How does the slope of the hill affect the gravitational force?

The slope of a hill does not directly affect the gravitational force. However, objects on steeper slopes will experience a greater component of the gravitational force pulling them downhill.

4. Is the gravitational force on a hill different from that on a flat surface?

The gravitational force on a hill is essentially the same as that on a flat surface. The difference lies in the direction of the force, as objects on a hill will experience a component of the force pulling them downhill.

5. Can I calculate the gravitational force on a hill using the same formula as on a flat surface?

Yes, the formula for calculating the gravitational force, F = mg, can be used on both flat surfaces and hills. However, it is important to take into account the slope of the hill when considering the direction of the force.

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