Incline with Pulley, find the mass of one block.

[Nirupt]

Homework Statement

A 20.0 kg block rests on a frictionless inclined plane of slope angle 30.0 degrees. A light cord attached to the block passes over a frictionlesss pulley at the top of the plane and is attached to a second block. What must be mass of the second block if the system is to be accelerating up and to the right at 2.00 m/s2?

https://dist-ed.waketech.edu/course...63858134f05bd87414264516909/InclineAtwood.png

Is a link to the image.

I found in class that the answer is 17.7 kg.. however I am stumped on where the numbers should go.

Homework Equations

The Attempt at a Solution

http://hyperphysics.phy-astr.gsu.edu/hbase/incpl.html#c1 is the link where I use my formulas

Well I do know that if I isolate the mass on the incline

ƩFnetx = -m1g * sin(30°) + Fτ = 2*20

I got 2*20 because of ma, and I know for m1g I substitute (20*9.8) I also know that acceleration is going up the incline, and if I were to remove the pulley and put them on the x-axis, it would be going to the right which is positive, therefore, the acceleration is positive.

Solving for that I get, Fτ = 138N which I know to be true

Now.. isolating m2 I get
ƩFnetx = -Fτ + m2g = 2m

however I have two masses??

In a previous problem when I had to find the mass of m2 if I wanted the objects to be at rest or constant velocity (so I assumed F=ma, but the sum would be 0). I ended up finding the weight of M2 being 98N.. would I plug that in for m2g? I guess not considering it doesn't give me the answer.. but I just wanted some feedback on this.

 

[PhanthomJay]

Homework Statement

A 20.0 kg block rests on a frictionless inclined plane of slope angle 30.0 degrees. A light cord attached to the block passes over a frictionlesss pulley at the top of the plane and is attached to a second block. What must be mass of the second block if the system is to be accelerating up and to the right at 2.00 m/s2?

https://dist-ed.waketech.edu/course...63858134f05bd87414264516909/InclineAtwood.png

Is a link to the image.

I found in class that the answer is 17.7 kg.. however I am stumped on where the numbers should go.

Homework Equations

The Attempt at a Solution

http://hyperphysics.phy-astr.gsu.edu/hbase/incpl.html#c1 is the link where I use my formulas

Well I do know that if I isolate the mass on the incline

ƩFnetx = -m1g * sin(30°) + Fτ = 2*20

I got 2*20 because of ma, and I know for m1g I substitute (20*9.8) I also know that acceleration is going up the incline, and if I were to remove the pulley and put them on the x-axis, it would be going to the right which is positive, therefore, the acceleration is positive.

Solving for that I get, Fτ = 138N which I know to be true

Now.. isolating m2 I get
ƩFnetx = -Fτ + m2g = 2m

however I have two masses??

In a previous problem when I had to find the mass of m2 if I wanted the objects to be at rest or constant velocity (so I assumed F=ma, but the sum would be 0). I ended up finding the weight of M2 being 98N.. would I plug that in for m2g? I guess not considering it doesn't give me the answer.. but I just wanted some feedback on this.

Your last equation should read ƩFnetx = -Fτ + (m_2)g = 2(m_2). Now do the algebra correctly to solve for m_2!

 

[Nirupt]

So I write the Equation..

m_2 = -138 + m_2g
--------------------
2

However, I still scratch my head at this, and I'm not sure if substituting would work either. Sorry if my algebra skills seem to be lacking... it is 1:37 a.m. where I am at currently.

 

[Bill Nye Tho]

Bring all of the mass dependant quantities to one side and factor it out. Divide the -Ft by accel - grav. You should end up with m_2 = (-138.1)/(2-9.81)

 

[Nickie]

Your approach is correct. To find the mass of m2, you need to use the equation ƩFnetx = -Fτ + m2g = 2m, but you also need to consider the force due to gravity acting on m1 (m1g) and the force due to tension in the string (Fτ). These forces will add up to equal the total force (2m) acting on the system. So your equation should look like this:

ƩFnetx = -m1g * sin(30°) + Fτ + m2g = 2m

Now you can plug in the values for m1, g, and the angle. You already know the value for Fτ (138N) and the acceleration (2m/s2). Solving for m2 will give you the mass of the second block.