A pulley and a wedge questions.

[MathematicalPhysicist]

from the attachment, i need to answer question 2.15c and 2.16.

here is what i did with the questions:

in the first question i got the next set of equations, which apparently are incorrect cause i didnt get the answer from the book:
T-uM1g=M1a
uM2g-T=M2a
M3g-T'=M3a'
T'=2T
2a'=a
wher a' is the accleration of mass M3 and a is of the other two, T' is the tension on M3 and T is the tension on the other two.

for the second question i got the next set of equations, which is also incorrect cause they for accelration with the respect to the y direction:
Nsin45=mg
mA+Ncos45=ma

thanks in advance.

 

[Doc Al]

You forgot the attachment.

 

[kyle8921]

I would like to clarify that the equations given in the question are correct. However, there may have been a misunderstanding in the way they were interpreted.

In the first question, the equations are representing the forces acting on the three masses attached to the pulley system. The correct equations should be:

T - M1g = M1a
M2g - T = M2a
T' - M3g = M3a'

Where T is the tension in the rope, M1 and M2 are the masses on either side of the pulley, and M3 is the mass attached to the pulley itself. The acceleration of M3, represented by a', is equal to twice the acceleration of the other two masses, represented by a. This is because the pulley is essentially doubling the force applied to M3. Therefore, the correct equations should be:

T - M1g = M1a
M2g - T = M2a
T' - M3g = 2M3a

In the second question, the equations are representing the forces acting on the wedge and the block on top of it. The correct equations should be:

mg - Nsin45 = ma
Ncos45 = mgsin45

Where m is the mass of the block and a is its acceleration. The normal force, N, is split into two components: one perpendicular to the surface of the wedge (Ncos45) and one parallel to the surface (Nsin45). The parallel component is equal to the force of gravity acting on the block (mgsin45) and the perpendicular component is equal to the force needed to accelerate the block (ma). Therefore, the correct equations should be:

mg - Nsin45 = ma
Ncos45 = mgsin45 + ma

I hope this clarifies any confusion and helps you arrive at the correct answers. Remember, it is important to carefully interpret and understand the equations given in a question before attempting to solve it.