How Do You Calculate Mass M1 in a Frictionless Pulley System?

[jeremy04]

Homework Statement

The pulley is light and frictionless. Find the mass M1, given that M2 (6.00 kg) is moving downwards and accelerates downwards at 3.61 m/s2, that θ is 30.0°, and that μk is 0.490.

Homework Equations

F=ma
F||=mg*cos(theta)
Fper=mg*sin(theta)

The Attempt at a Solution

I have no idea where to start this problem..

I know how to find F|| and Fperendicular when there's no pulley/no friction.. no idea where to start..

 

[learningphysics]

Take the freebody diagram of M1... write $$\Sigma\vec{F_x} = m\vec{a_x}$$ and $$\Sigma\vec{F_y} = m\vec{a_y}$$ where x is along the plane, and y is perpendicular to the plane.

similarly write an F=ma equation for M2.

 

[m2003]

I would first identify the knowns and unknowns in this problem. The knowns are M2, the acceleration, the angle θ, and the coefficient of kinetic friction μk. The unknown is the mass M1.

Next, I would use the equations of motion to set up a system of equations to solve for M1. Since M2 is moving downwards and accelerating, we can use the equation F=ma to find the net force acting on M2. This net force is equal to the sum of the parallel and perpendicular forces, F|| and Fperpendicular.

The parallel force, F||, is equal to the weight of M2 multiplied by the cosine of the angle θ. This can be written as F||=M2g*cos(θ). Similarly, the perpendicular force, Fperpendicular, is equal to the weight of M2 multiplied by the sine of the angle θ. This can be written as Fperpendicular=M2g*sin(θ).

Since the pulley is light and frictionless, we can assume that there is no friction force acting on the system. Therefore, the net force on M2 is equal to the parallel force, F||. This can be written as F=M2g*cos(θ).

We can now substitute this expression for F into the equation F=ma and solve for M1. This would give us the equation M2g*cos(θ)=M1a. We can then substitute the given values of M2, θ, and a into this equation and solve for M1.

In summary, as a scientist, I would approach this problem by identifying the knowns and unknowns, using the equations of motion to set up a system of equations, and solving for the unknown using the given values and equations.