How can F = mg sin. θ be proven on a smooth plane?

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In summary, the formula for calculating force (F) using mass (m), gravity (g), and angle (θ) is F = mg sin(θ). The variables represent the mass of the object in kilograms, the acceleration due to gravity in meters per second squared, and the angle at which the force is applied. To use this formula, you will need to know these values and plug them in to solve for F. The units used for each variable are kilograms (kg) for mass, meters per second squared (m/s²) for gravity, and degrees or radians for angle. The significance of the angle (θ) in this formula is that it represents the direction in which the force is being applied, which affects the magnitude of
  • #1
DarkNess_wtc
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i can't understand the formula

F = mg sin. θ

on a smooth plane

how to proof a = g sin. θ

sin. θ...




http://img213.imageshack.us/img213/2313/44877072.jpg
 
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  • #2
Do you understand how to find the components of a vector using trig functions of a right triangle?

You might want to read this: http://www.physicsclassroom.com/Class/vectors/u3l3e.cfm"

Ask yourself:
What forces act on the object? What are their components parallel and perpendicular to the incline? What's the net force on the object? Then apply Newton's 2nd law.
 
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  • #3
oic...

thanks for your ans
 

FAQ: How can F = mg sin. θ be proven on a smooth plane?

What is the formula for calculating force (F) using mass (m), gravity (g), and angle (θ)?

The formula for calculating force is F = mg sin(θ).

What does each variable in the formula represent?

m represents the mass of the object in kilograms, g represents the acceleration due to gravity in meters per second squared, and θ represents the angle at which the force is applied.

How do I use this formula to calculate force?

To calculate force, you will need to know the mass of the object in kilograms, the acceleration due to gravity (which is usually given as 9.8 m/s²), and the angle at which the force is being applied. Once you have these values, simply plug them into the formula F = mg sin(θ) and solve for F.

What units are used for each variable in the formula?

The mass (m) is measured in kilograms (kg), the acceleration due to gravity (g) is measured in meters per second squared (m/s²), and the angle (θ) is measured in degrees or radians, depending on the unit of measurement being used.

What is the significance of the angle (θ) in this formula?

The angle (θ) represents the direction in which the force is being applied. This is important because the force will have a different magnitude depending on the angle at which it is applied. For example, if the angle is 90 degrees, the force will be equal to mg. However, if the angle is less than 90 degrees, the force will be less than mg.

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