Question

Blocks A and B of unknown masses m1 and m2, respectively, are set up on an inclined plane as shown. Block A is attached to block B by a light string that passes over an ideal pulley. Block A is on a surface of negligible friction. The blocks are released from rest, block A accelerates up the incline, and its acceleration a is measured. Which of the following uses the data for the magnitude of the acceleration to support a correct claim about the masses of the blocks?
If a>gsinθ , then m1>m2.


Answer A: If a is greater than g sine theta , then m sub 1 is greater than m sub 2 .

A


If am2.


Answer B: If a is less than g sine theta , then m sub 1 is greater than m sub 2 .

B


If a>gsinθ, then m1

Answer 1

Newton's second law we can find that the correct answer is:  

 E)  It cannot be determiner whick block has more masses from the information provided

Newton's second law establishes the relationship between force, mass, and acceleration of a body. Since force and acceleration are vector quantities, their components must be added on each axis

For this problem we have two bodies, let's write Newton's second law for the body B, we assume that the body B descends

            W_b - T = m_b a

            W_b  = m_b g

            m_b - T = m_b a

Where W_b is the weight of block B, T the tension of the string, mb the mass of block b and the acceleration

Now let's find the relation for block A

let's set a datum with the x axis parallel to the ramp

           T - Wₓ = mₐ a

           sin θ = Wₓ / W

            Wₓ = Wₐ sin θ

             Wₐ = mₐ g

Where Wₓ is the component of the weight, Wₐ the weight of the body A and θ the angle of the plane

Let's write our system of equations

           m_b g - T = m_b a

           T - mₐ g sin θ = mₐ a

let's add the equations

            g (m_b - mₐ sin θ) = (m_b + mₐ) a

            a =   $\frac{m_b - m_a \ sin \ \theta}{m_b+m_a} \ g$

Let's analyze this expression

• The numerator is positive the body B descends, this occurs when

          m_b - mₐ sin θ > 0

           

• The numerator is negative, body B rises

           m_b - mₐ  sin θ <0

We can observe that the acceleration is positive or negative depending on the relation of the masses and the angle of the plane.

In conclusion using Newton's second law we find that the correct answer is  

 E )   It cannot be determiner whick block has more masses from the information provided

learn more about Newton's second law here:

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