# Dynamics problem involving an inclined plane and Friction

• Alencarina
In summary, the conversation was about trying to calculate the horizontal forces involved in a scenario where a wedge is accelerating to the right. The equation f + Wx - Fy = 0 was used to represent the forces, but there was confusion about whether the acceleration was of the block or the plane. The figure given suggested that something was causing the wedge to accelerate, reducing the normal force on the block and therefore the maximum frictional force. The speaker was unsure about the choice of reference frame and axes, and requested clarification.
Alencarina
Homework Statement
An inclined plane shown in the figure has the acceleration intensity of a, to the right. Show that the block will slide on the plane if a > g tan ( θ - α ), where μs ( static friction) = tan θ is the static friction coefficient between the contact surfaces.
Hi, it's a simple(maybe) question.
Relevant Equations
F= ma
f= μN
So after trying to calculate the horizontal forces to solve it:

f + Wx(gravity force component of x) - Fy ( the Force that is supposedly giving the the acceleration) = 0

It got to me that the question said "plane has the acceleration" is that even possible? Unless the plane is another object like a ramp, but the plane itself? it's like considering the Earth's movement?!
I kept trying to prove continuing the horizontal forces. If a= g tan ( θ - α ) it means it won't move, so friction will be the μs= tan θ and the Fnet will be zero.

f + Wx - Fy =0

μN + mgcos θ - masinθ = 0

μ(mgcosθ + macosθ) - masinθ =0
And it just went on to a complex thing, I tried a couple of times, the results were close of g tan ( θ - α ), but I got to be doing something wrong.

Summarizing, could anyone tell me is the acceleration of the block or the plane? Is the block is sliding down or up (what??) and am I even close with that thought?
Figure given:

You are supposed to assume that something, doesn't matter what, is causing the wedge to accelerate to the right. This reduces the normal force on the block, and hence reduces the max frictional force.
Just consider the acceleration of the block and the forces on it.
Choose either an inertial frame or the reference frame of the wedge.
For axes, choose either horizontal and vertical or parallel and normal to the plane.

## 1. How do you calculate the force of friction on an inclined plane?

The force of friction on an inclined plane can be calculated using the formula F = μN, where μ is the coefficient of friction and N is the normal force. The normal force can be found by multiplying the mass of the object by the acceleration due to gravity and the cosine of the angle of incline.

## 2. What is the role of friction in a dynamics problem involving an inclined plane?

Friction plays a significant role in dynamics problems involving an inclined plane because it acts in the opposite direction of motion and can either increase or decrease the net force on an object. It also affects the acceleration and velocity of the object as it moves along the plane.

## 3. How does the angle of incline affect the dynamics of an object on an inclined plane?

The angle of incline has a direct impact on the dynamics of an object on an inclined plane. As the angle increases, the force of gravity acting on the object perpendicular to the plane decreases, resulting in a decrease in the normal force and an increase in the force of friction. This can affect the acceleration and velocity of the object.

## 4. What is the difference between kinetic and static friction on an inclined plane?

Kinetic friction is the force of friction acting on an object in motion, while static friction is the force of friction acting on an object at rest. On an inclined plane, the force of kinetic friction is typically less than the force of static friction, as the object must overcome the initial resistance of static friction to start moving.

## 5. How does the coefficient of friction affect the dynamics of an object on an inclined plane?

The coefficient of friction is a measure of the roughness or smoothness of the surfaces in contact and can greatly affect the dynamics of an object on an inclined plane. A higher coefficient of friction means a greater force of friction, which can slow down the object and decrease its acceleration. A lower coefficient of friction means a smaller force of friction, allowing the object to move more easily along the plane.

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