Is Fg the Only Force to Consider for Ft4 in a Pulley System?

[N_L_]

I have some questions about the following problem:

I know that Ft1 and Ft2 are equal. Is Fg the only force that needs to be taken into account for Ft4? Does the force being applied to lift the piano need to be taken into account for Ft3? If not, is it just m*g?

http://img96.imageshack.us/img96/8798/782tm.jpg

 

[Chi Meson]

Assuming that the pulleys are frictionless, the tension is the same throughout the rope (frictionless pulleys can be found only in textbook problems).

Also assuming that the piano is moving at a constant speed, F_T4 is equal to the weight of the piano. More force here is necessary to accelerate the piano upward.

Look at the top pully: how many strands are pulling it down? How much tension in each strand? ("strand" = "rope segment")

 

[kyle8921]

I would approach this problem by first identifying all the forces acting on the system. In this case, we have the force of gravity (Fg) acting downwards on the piano, and the tension forces (Ft1, Ft2, Ft3, Ft4) acting in different directions due to the pulleys.

To answer your first question, yes, Ft1 and Ft2 are equal because they are connected by a rope and are part of the same system. This can be explained by Newton's Third Law, which states that for every action, there is an equal and opposite reaction. In this case, the force exerted by the rope on the pulley (Ft1) will be equal and opposite to the force exerted by the pulley on the rope (Ft2).

Moving on to your second question, Fg is not the only force that needs to be taken into account for Ft4. We also need to consider the force being applied to lift the piano (Fap), which is connected to the rope and ultimately contributes to the tension force at Ft4. This can be seen in the free body diagram of the piano, where Fg and Fap are shown as separate forces acting on the piano.

Lastly, you are correct in assuming that the force being applied to lift the piano (Fap) can be represented by m*g, where m is the mass of the piano and g is the acceleration due to gravity. However, we also need to take into account the direction of this force, which will ultimately contribute to the direction and magnitude of the tension force at Ft3.

In summary, to solve this problem, we would need to consider all the forces acting on the system and use Newton's Laws of Motion to determine the relationship between these forces. I hope this helps clarify the concepts involved in this force tension/pulley problem.