# Find Mass M1 Given Acceleration, Angle, and Friction

• thatguy101
In summary, the mass of M1 is 2.38 kg given that M2 accelerates downwards at 2.31 m/s^2, q is 20°, and μk is 0.41.
thatguy101

## Homework Statement

M1 and M2 are two masses connected as shown (M2 hangs over the table). The pulley is light (massless) and frictionless. Find the mass M1, given that M2 (3.0 kg) accelerates downwards at 2.31 m/s^2, q is 20°, and μk is 0.41.

F=ma
μn=friction

## The Attempt at a Solution

Well I thought I could find tension using F=3*2.31 but that didn't get me anywhere. I drew a force diagram for m1, but it looks like there's too much missing to be able to continue. Is the tension part at least right?

hi thatguy101! welcome to pf!

(we usually use "T" for tension )
thatguy101 said:
Well I thought I could find tension using F=3*2.31

is that Ftotal = ma?

so then would I subtract gravity?
Ft=3*2.31-3*9.81?

Why not give us the diagram so that we know what q = 20$^{o}$ refers to?

Sorry. It's suppose to say θ.
m1 is on an incline of 20°, and m2 is hanging off the incline.

Ok so my diagram looks like this.
For m1 I have forces in the y direction as y: Fg*cosθ-Fn=0
And the forces in the x direction as x:Ft-Fg*sinθ-Ff=a.
And then for m2 there are none in the x direction but for y I have y: Fg-Ft=ma.
Am I right so far?

thatguy101 said:
Ok so my diagram looks like this.
For m1 I have forces in the y direction as y: Fg*cosθ-Fn=0
And the forces in the x direction as x:Ft-Fg*sinθ-Ff=a.
And then for m2 there are none in the x direction but for y I have y: Fg-Ft=ma.
Am I right so far?

yes, except in your second equation, you need to check the signs (and you forgot to write the m before the a)

Thank you. I figured it out.
so Ft=mg*sinθ+μ*mg*cosθ+ma
factor out the m, Ft=m(g*sinθ+μ*g*cosθ+a)
then solved for m. and since Ft= m2g-m2a, I just put in the numbers and came up with 22.47 N amd just plugged in everything else into the equation above and got 2.38 kg

## 1. What is the equation for finding mass (M1) given acceleration, angle, and friction?

The equation for finding mass (M1) in this scenario is M1 = (Ff - Fsinθ)/a, where Ff is the force of friction, θ is the angle of inclination, and a is the acceleration.

## 2. How do I determine the force of friction (Ff) in this equation?

The force of friction (Ff) can be determined by multiplying the coefficient of friction (μ) by the normal force (Fn). This can be represented as Ff = μFn.

## 3. What is the significance of the angle of inclination (θ) in this equation?

The angle of inclination (θ) represents the angle at which the object is being pulled or pushed. It affects the amount of force needed to move the object and is necessary in determining the mass (M1) in this equation.

## 4. Can this equation be used for any type of object or surface?

This equation can be used for objects on inclined surfaces with a constant coefficient of friction. It may not be applicable for objects on non-uniform surfaces or surfaces with changing friction.

## 5. How accurate is this equation in determining the mass (M1) of an object?

The accuracy of this equation depends on the accuracy of the values used for acceleration, angle, and friction. It is important to measure these values accurately for a more precise result.

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