# Acceleration at incline with friction

In summary, the block of mass 250 kg is placed on inclines of different angles and materials with coefficients of friction. The static friction is marginally higher than the kinetic friction. The magnitude of acceleration for each incline, from smallest to largest, is as follows: B, D, E, A, C.

## Homework Statement

A block of mass 250 kg is placed at rest onto 5 different inclines. The angle of incline A is
22o,
B is at 22o,
C is at 22o,
D is at 10o, and
E is at 10o.
The inclines are made of different materials, and have coefficients of friction
mkA = 0.3,
mkB = 0.4,
mkC = 0.5,
mkD = 0.2, and
mkE = 0.1.
For each incline, the static friction is only marginally higher than the kinetic friction.
Rank the magnitude of the acceleration of the block on each incline, from smallest to largest. For ties, list answers alphabetically.

## Homework Equations

F=ma
Frictional force equation

## The Attempt at a Solution

I tried and got these values: A: .945224m/s^2
B: .036584m/s^2
C: -.872056m/s^2
D: -.228472m/s^2
and E: .73664m/s^2

so I tried C,D,B,E,A but it was wrong :-(

Try B again, it doesn't look like you've calculated it correctly.

## 1. What is the formula for calculating acceleration at an incline with friction?

The formula for calculating acceleration at an incline with friction is a = (mgsinθ - μmgcosθ) / (m + msinθ), where a is the acceleration, m is the mass of the object, g is the acceleration due to gravity, θ is the angle of the incline, and μ is the coefficient of friction.

## 2. How does the angle of incline affect the acceleration at an incline with friction?

The angle of incline affects the acceleration at an incline with friction because as the angle increases, the component of gravity acting parallel to the incline decreases, leading to a decrease in acceleration. This is reflected in the formula for acceleration, where the sine of the angle is in the numerator and the cosine of the angle is in the denominator.

## 3. What role does friction play in the acceleration at an incline with friction?

Friction plays a significant role in the acceleration at an incline with friction. It is represented in the formula for acceleration as the coefficient of friction multiplied by the normal force, which is the force perpendicular to the incline. Friction acts in the opposite direction of motion and can therefore decrease the acceleration of an object.

## 4. How does the mass of the object affect the acceleration at an incline with friction?

The mass of the object affects the acceleration at an incline with friction through its influence on the normal force. The normal force is equal to the weight of the object, which is directly proportional to its mass. Therefore, as the mass increases, so does the normal force, resulting in a larger denominator in the acceleration formula and a smaller acceleration.

## 5. How can the coefficient of friction be determined for a specific surface?

The coefficient of friction for a specific surface can be determined through experimentation. The most common method is to use a force sensor to measure the force required to move an object across the surface at a constant velocity. The coefficient of friction can then be calculated by dividing the measured force by the weight of the object. It is important to note that the coefficient of friction may vary depending on the surface conditions, such as roughness or moisture.

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