# Solving Accelerated Block Problem with Friction & Angle Alpha

• Kruger
In summary, in this conversation, the problem involves determining a specific acceleration that will prevent a blue block from slipping relative to a red block with mass m1, given a coefficient u1 of friction between the two blocks. The relevant equations are Newton's equations, and the solution involves balancing forces and drawing a force diagram. The acceleration must be such that the sum of all forces acting on the block is horizontal with a magnitude of ma. The range of accelerations that will prevent slipping depends on whether friction acts up or down the plane.
Kruger
A block is accelerated with a, take a look at the picture. There is a friction between the red block and the other one with mass m1. The friction is given by the coefficient u1.

I have to determine a such that the blue block is not moving relative to the red one. a has to bi in depenence of angle alpha.

## Homework Equations

The relevant equations are basically Newton's equations.

## The Attempt at a Solution

What I have done so far is the following: One force acting on the block is coming from the gravitational field, so F_g=m1*g. I have splitted this one in components: F||=sin(alpha)*F_g and (already added friction) F_s=cos(alpha)*F_g*(1-u1).

I don't know how I can go on. The basic problem is I don't really know how a acts one the block. And how I've to balance the forces.

#### Attachments

• Unbenannt.JPG
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There will be a range of accelerations that will prevent the block from slipping because friction can act either up the plane or down the plane. Are you supposed to be finding the minimum accleration, maximum acceleration, or both?

You know the blue block must have the same acceleration as the red ramp. Draw all of the forces acting on the block. The sum of all the forces must be horizontal and have magnitude ma.

I would approach this problem by first identifying all the relevant forces acting on the system. In this case, we have the force of gravity acting on the mass m1, the normal force from the surface on which the block is resting, and the friction force between the two blocks. We can also consider the force of tension in the string connecting the two blocks, but it may not be relevant to the problem at hand.

Next, I would apply Newton's second law, which states that the net force on an object is equal to its mass times its acceleration. In this case, we can write the equation for the red block as:

ΣF = m1a = F_g - F_s

Where ΣF represents the sum of all the forces acting on the block, m1 is its mass, and a is its acceleration. The force of gravity, F_g, can be broken down into its components as you have already done. The friction force, F_s, can also be expressed as you have shown, but we must also consider the normal force, which is equal in magnitude but opposite in direction to the friction force.

Once we have this equation, we can solve for the acceleration, a, in terms of the angle alpha and the coefficient of friction, u1. This will give us the required acceleration to keep the blue block stationary relative to the red block.

In general, when solving problems in physics, it is important to clearly identify all the relevant forces and apply the appropriate equations to solve for the unknown quantities. It may also be helpful to draw a free-body diagram to visualize the forces acting on the system.

## 1. What is the "accelerated block problem with friction & angle alpha"?

The accelerated block problem with friction and angle alpha is a physics problem that involves calculating the motion of a block on an inclined plane with friction. It is a commonly used example in introductory physics courses to demonstrate the application of Newton's laws of motion.

## 2. How do you solve the accelerated block problem with friction & angle alpha?

To solve this problem, you would first draw a free body diagram of the block and identify all the forces acting on it, such as the force of gravity, normal force, and frictional force. Then, you would use Newton's second law (F=ma) to determine the net force acting on the block and the resulting acceleration. Finally, you can use the kinematic equations to calculate the displacement, velocity, and time of the block's motion.

## 3. What is the significance of angle alpha in the accelerated block problem?

Angle alpha represents the angle of incline of the plane on which the block is moving. It affects the magnitude of the normal force and the frictional force acting on the block, thus influencing the block's acceleration and motion.

## 4. How does friction impact the motion of the block in this problem?

Friction is a force that opposes the motion of the block and is caused by the interaction between the block and the surface of the inclined plane. It reduces the acceleration of the block and can even cause it to remain stationary if the force of friction is greater than the applied force.

## 5. What are some real-life applications of the accelerated block problem with friction & angle alpha?

The concepts and principles used to solve this problem can be applied to many real-life situations, such as calculating the motion of a car moving up or down a hill, determining the angle of inclination needed for a car to safely travel on a curved road, and understanding the motion of objects sliding down a ramp or ski slope.

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