Particle on a slope with friction question

In summary: Friction coefficient = sine ( incline angle ) / cosine ( incline angle )In summary, the conversation discusses a poorly written question about a box on a slope and its minimum angle for slipping, as well as various calculations and concepts related to mechanics and dynamics. The main focus is on finding the relationship between the gravitational force and the friction force, and using that to determine the minimum angle for slipping. The conversation also touches on the use of symbols and proper notation in solving the problem.
  • #1
Jackelkes95
2
0
Hi guys! I am really struggling with this poorly written question. Any help would be appreciated!
a 3.5 kg box is on a slope. What is the minimum angle which will cause the box to slip if μ (friction) =0.6? If the plane is tilted to an angle of θ above this slipping value what is the acceleration on the box when θ is 10 degrees and -10 degrees (below). How long will it take the box to stop if θ = -10 degrees with an initial velocity of 2 m/s and with θ = 10 degrees how far will the box slide in that time starting from rest?
 
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  • #2
Can you try the first part about finding the minimum angle?
 
  • #3
This is standard mechanics. m*g is straight down, the friction is dependent on the force normal to the slope and the accelerating force is parallel to the slope.
 
  • #4
If i was given the angle i can easily calculate the forces parallel and perpendicular to the slope ie mgcosθ for perpendicular resultant force. I just haven't a clue how to go about this question! Dynamics are not my forte.
 
  • #5
Jackelkes95 said:
ie mgcosθ for perpendicular resultant force.
Yes - just continue...
 
  • #6
Jackelkes95 said:
mgcosθ for perpendicular resultant
Be careful about reusing symbols with different meanings. I assume here you mean theta as the angle of an arbitrary slope, but in the question it is the additional angle of the slope beyond a critical angle.
 
  • #7
I can get you started.
The point at which it breaks stasis is when the forces up and down the incline are equal.
So:
Gravitational force = friction force
( m * g * sine ( incline angle ) ) = ( m * g * cosine ( incline angle ) * friction coefficient )
Transpose for friction coefficient
 

Related to Particle on a slope with friction question

1. What is a particle on a slope with friction?

A particle on a slope with friction is a physical scenario where a single point-like particle is placed on an inclined surface and experiences both the force of gravity and friction from the surface. This setup is commonly used in physics problems to illustrate concepts such as equilibrium, forces, and motion.

2. How do you calculate the net force on a particle on a slope with friction?

To calculate the net force on a particle on a slope with friction, you must first find the force of gravity acting on the particle, which is equal to its mass multiplied by the acceleration due to gravity (9.8 m/s^2). Then, you must determine the frictional force, which is equal to the coefficient of friction multiplied by the normal force (force perpendicular to the slope). The net force is then calculated by adding the forces in the direction of motion and subtracting the forces in the opposite direction.

3. How does friction affect the motion of a particle on a slope?

Friction plays a critical role in the motion of a particle on a slope. It acts in the opposite direction of motion, slowing down the particle and eventually causing it to come to a stop. The amount of friction depends on the coefficient of friction and the normal force, which is affected by the slope angle and the mass of the particle. A higher coefficient of friction or a steeper slope will result in a greater frictional force and a shorter distance traveled by the particle.

4. What is the coefficient of friction in a particle on a slope with friction?

The coefficient of friction is a measure of the amount of resistance between two surfaces in contact. In the case of a particle on a slope with friction, it represents the ratio of the frictional force to the normal force. It varies depending on the type of surface and the materials in contact. For example, a particle on a wooden slope will have a different coefficient of friction than one on a metal slope.

5. How does the angle of the slope affect the motion of a particle on a slope with friction?

The angle of the slope has a significant impact on the motion of a particle on a slope with friction. As the angle increases, so does the component of the force of gravity acting in the direction of motion. This results in a higher net force and a faster acceleration of the particle. However, as the angle approaches 90 degrees, the normal force decreases, causing the frictional force to decrease as well. This results in a lower net force and a slower acceleration of the particle.

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