Finding Accerleration on a slope with friction

[fallen186]

**Sorry the latex didn't really work for me.**

Homework Statement

In the figure below, m1 = 3.6 kg, m2 = 5.1 kg, and the coefficient of kinetic friction between the inclined plane and the 3.6-kg block is μk = 0.25. Find the magnitude of the acceleration of the masses.

m1 = 3.6 kg
m2 = 5.1 kg
μ = 0.25
Theta = 30

Homework Equations

a = ((m2*g)-(m1*g*sin(theta)))/(m1+m2)

The Attempt at a Solution

Since there is friction I did [tex] (m1*g*sin(theta)-μ*Fn
Fn = (.5*m1*g*3^.5)

a = ((5.1 kg*9.8 m/s^2) - (3.6 kg*9.8 m/s^2*sin(30)-.25(.5*3.6kg*9.8m/s^2*3^.5)))/(3.6kg+5.1kg)
a = (50.031- (17.658 - 7.638))/(8.7)

a = 4.599 m/s^2

I got this wrong. please help

 

[alphysicist]

Hi fallen186,

**Sorry the latex didn't really work for me.**

Homework Statement

In the figure below, m1 = 3.6 kg, m2 = 5.1 kg, and the coefficient of kinetic friction between the inclined plane and the 3.6-kg block is μk = 0.25. Find the magnitude of the acceleration of the masses.

m1 = 3.6 kg
m2 = 5.1 kg
μ = 0.25
Theta = 30

Homework Equations

a = ((m2*g)-(m1*g*sin(theta)))/(m1+m2)

The Attempt at a Solution

Since there is friction I did [tex] (m1*g*sin(theta)-μ*Fn

There's not much detail about the problem, but the minus sign here means that m1 is moving down the incline. Is that what you intended?

 

[baba89]

I would first check to make sure all of my units are consistent. In your attempt at a solution, it looks like you have some inconsistencies in your units. For example, in the equation for Fn, you have used the square root of 3 in meters, but in your calculations for the forces, you are using the value of 3.6 kg for m1 instead of the square root of 3. This could be why you are getting a different answer than expected.

Additionally, when dealing with friction, it is important to remember that the force of friction is always in the opposite direction of motion. In this case, the 3.6 kg block is moving down the incline, so the force of friction would be acting up the incline, not down as you have it in your calculations.

I would also double check your calculations for the force of friction. It looks like you may have mixed up the coefficient of friction (μ) with the normal force (Fn). The correct equation for the force of friction would be μ*Fn.

Once you have checked for any inconsistencies and corrected any errors in your calculations, you should be able to find the correct magnitude of acceleration for the masses. Remember to always double check your work and use units consistently to ensure accurate results.