Dynamics: Incline Slope Derivation Simplification

In summary, the conversation was about a physics problem involving a study guide with a fill-in-the-blanks section and an extended simplification blank. The problem had no given values and described a standard block on a standard slope with a north-east applied force pushing down on the block, not parallel to the horizontal or vertical axis. The equations discussed were Fnet = ma, Fnormal = Fay + Fgy, Fnormal = (Fapplied)(sinØ) + (Fgravity)(cosØ), Fnet = Fax - Fgx - Ffk, and Fnet = (Fapplied)(cosØ) - (Fgravity)(sinØ) - (Uk)(Fnormal). The conversation also included a
  • #1
Asleky
7
0

Homework Statement


No official problem, just a study guide fill-in-the-blanks with an extended simplification blank. Basically, no values were given, and it is a standard block on a standard slope with a north-east applied force pushing down on the block (not parallel to horizontal or vertical axis).

Homework Equations


Fnet = ma
Fnormal = Fay + Fgy
Fnormal = (Fapplied)(sinØ) + (Fgravity)(cosØ)
Fnet = Fax - Fgx - Ffk
Fnet = (Fapplied)(cosØ) - (Fgravity)(sinØ) - (Uk)(Fnormal)

The Attempt at a Solution


He asked us to substitute the second equation above into the third equation above. I am terrible at simplifying and so this is as far as I've gotten:
ma = (Fapplied)(cosØ) - (Fgravity)(sinØ) -Uk(Fapplied)(sinØ) + (Fgravity)(cosØ)
This is extremely messy and confusing, I am aware, so I am in deep gratitude to anyone taking time to help a scrub physics student like me. :D Thank you so much for any simplifying advice! I am solving for acceleration.
 
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  • #2
Actually upon further inspection, could I somehow make it (Fapplied)(tanØ) and (Fgravity)(tanØ)? I am confident that the trig law tanØ = sinØ/cosØ will be used. At least I'm on to something :(
 
  • #3
The arrangement is not clear. Are you saying that the force is acting down the slope and parallel to it?
According to this equation
Asleky said:
Fnormal = (Fapplied)(sinØ) + (Fgravity)(cosØ)
the applied force is horizontal.
 
  • #4
haruspex said:
The arrangement is not clear. Are you saying that the force is acting down the slope and parallel to it?
According to this equation
the applied force is horizontal.
Yeah that's why I multiplied by sin and cos to make all the components on one axis.
 
  • #5
haruspex said:
According to this equation ... the applied force is horizontal.
Asleky said:
Yeah that's why I multiplied by sin and cos to make all the components on one axis.
But you wrote in the OP:
Asleky said:
with a north-east applied force pushing down on the block (not parallel to horizontal or vertical axis)
So which is it? Is the applied force horizontal or at an angle?
 
  • #6
Could you draw a FBD?
 

Related to Dynamics: Incline Slope Derivation Simplification

1. What is the formula for calculating the acceleration of an object on an inclined slope?

The formula for calculating the acceleration of an object on an inclined slope is a = gsinθ, where a is the acceleration, g is the acceleration due to gravity (9.8 m/s^2), and θ is the angle of the slope.

2. How is the acceleration of an object on an inclined slope affected by the slope's angle?

The acceleration of an object on an inclined slope is directly proportional to the sine of the angle of the slope. This means that as the angle of the slope increases, the acceleration of the object also increases.

3. What is the difference between a ramp and an incline slope in terms of dynamics?

In terms of dynamics, a ramp and an incline slope are essentially the same. Both have a slope or angle that affects the acceleration of an object moving along it. However, a ramp is typically longer and more gradual, while an incline slope is steeper and shorter.

4. How can the equation for calculating acceleration on an incline slope be simplified?

The equation for calculating acceleration on an incline slope, a = gsinθ, can be simplified by using trigonometric identities. For example, if the slope's angle is 30 degrees, the equation can be simplified to a = (g/2). This simplification is useful for quick calculations and problem-solving.

5. What is the significance of understanding dynamics on an incline slope?

Understanding dynamics on an incline slope is important in many real-world situations, such as calculating the speed and distance of a car driving up a hill or the acceleration of a ball rolling down a ramp. It also helps to understand the relationship between forces, angles, and motion, which is crucial in many fields of science and engineering.

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