Resolving alpha with friction and angles

In summary, the conversation discusses a situation where an object of weight 1250N is placed on a straight footpath with an angle of alpha with the horizontal. The coefficient of friction is 0.1 and the minimum force required to keep the object at rest on the footpath is 50N. By treating the object as a particle, the value of alpha is found to satisfy the equation 10sin(alpha)-cos(alpha)=0.4. The individual has drawn a free body diagram and labeled all forces, but is unsure of what to do next and has asked for guidance.
  • #1
bob4000
40
0
a straight footpath makes an angle of aplha with the horizontal. an object P of weight 1250N rests on footpath. the coefficient of friction is 0.1. the least magnitude of a force, acting up the footpath, which will hold the object at rest on the footpath is 50N. by treating the object as a particle show that the value of alpha satisfies 10sinaplha-cosalpha=0.4

i have drawn FBD and labbelled all of the forces and tried to solve for alpha using simultaneous equations and other methods (the names of which I am not too sure). could anyone please tell me what to do next?

much obliged
 
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  • #2
Post your work, so we can see exactly where you are.
 
  • #3
f=ma parallel to slope

50-F-1250sinaplha=0

f=ma perpendicular to slope

N-1250cosalpha=0

F=mu*N
mu=0.1
N=F/mu;N=10F
; 10F-1250cosalpha=0
F+1250sinalpha=50

ps, I am half asleep so excuse any blatant stupidity
 

1. What is the significance of resolving alpha with friction and angles?

Resolving alpha with friction and angles is an important concept in physics and engineering. It helps us understand the forces acting on objects and how they affect motion and stability.

2. How do we calculate alpha with friction and angles?

To calculate alpha with friction and angles, we need to use trigonometric functions and equations that take into account the angle of the surface and the coefficient of friction between two surfaces. This allows us to determine the magnitude and direction of the forces acting on the object.

3. What is the difference between resolving alpha with friction and angles and resolving alpha without friction?

When resolving alpha without friction, we only consider the forces acting perpendicular to the surface, while ignoring the effects of friction. However, when resolving alpha with friction and angles, we take into account the frictional force, which can greatly affect the object's motion and stability.

4. How does the angle of the surface affect resolving alpha with friction and angles?

The angle of the surface has a significant impact on resolving alpha with friction and angles. The steeper the angle, the greater the component of the force acting parallel to the surface, which can affect the motion and stability of the object. Additionally, the angle can also affect the magnitude and direction of the frictional force.

5. In what real-world situations is resolving alpha with friction and angles useful?

Resolving alpha with friction and angles is useful in many real-world situations, such as calculating the force needed to push a heavy object up a ramp, determining the stability of a structure on an inclined plane, or analyzing the motion of a car on a curved road. It is also important in understanding the dynamics of objects such as ski slopes, roller coasters, and airplanes.

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