Ablock of mass m1 = 288.0 kg sits on an inclined plane and is connected to a bucket with a massless string over a massless and frictionless pulley. the coefficient of static friction between the block and the plane is μs = 0.41, and the angle between the plane and the horizontal is θ = 41°. mass m2 can be changed by adding or taking away sand from the bucket. what is the maximum value of m2 for which the system will remain at rest?

M2 = 278.06 kg

Explanation:

We calculate the weight of M1

W=m*g

Where

m: mass (kg)

g: acceleration due to gravity (m/s²)

W₁=288* 9.8= 2822.4 N

Look at the attached graphic

We calculate the x-y components of the weight :

W₁x= 2822.4*sin41° N =1851.66 N

W₁y= 2822.4 *cos41° N = 2130.09 N

We apply Newton's first law for the balance in M1:

Σ Fy=0

Fn-W₁y=0  ,   Fn: normal force

Fn=W₁y=2130.09N

Friction Force = Ff=μs *Fn = 0.41*2130.09 =873.34 N

Σ Fx=0

T- W₁x- Ff=0

T= 1851.66 + 873.34

T= 1851.66 + 873.34

T=2725 N

We apply Newton's first law for the balance in M2:

Σ Fy=0

T- W₂ =0

W₂ = T = 2725 N

W₂ = M2*g

M2 = W₂/g

M2 = 2725/9.8

M2 = 278.06 kg

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